Subsets of configurations and canonical partition functions
DEFF Research Database (Denmark)
Bloch, J.; Bruckmann, F.; Kieburg, M.;
2013-01-01
We explain the physical nature of the subset solution to the sign problem in chiral random matrix theory: the subset sum over configurations is shown to project out the canonical determinant with zero quark charge from a given configuration. As the grand canonical chiral random matrix partition f...... function is independent of the chemical potential, the zero-quark-charge sector provides the full result. © 2013 American Physical Society....
Narasimhan, S L; Krishna, P S R; Ponmurugan, M; Murthy, K P N
2008-01-01
We have explained in detail why the canonical partition function of interacting self-avoiding walk (ISAW) is exactly equivalent to the configurational average of the weights associated with growth walks, such as the interacting growth walk (IGW), if the average is taken over the entire genealogical tree of the walk. In this context, we have shown that it is not always possible to factor the density of states out of the canonical partition function if the local growth rule is temperature dependent. We have presented Monte Carlo results for IGWs on a diamond lattice in order to demonstrate that the actual set of IGW configurations available for study is temperature dependent even though the weighted averages lead to the expected thermodynamic behavior of ISAW. PMID:18190183
A simple way of approximating the canonical partition functions in statistical mechanics
Fernández, Francisco M.
2015-09-01
We propose a simple pedagogical way of introducing the Euler-MacLaurin summation formula in an undergraduate course on statistical mechanics. The reason is that the students may feel more comfortable and confident if they are able to deduce the main equations. To this end we put forward two alternative routes: the first one is the simplest and yields the first two terms of the expansion. The second one is somewhat more elaborate and takes into account all the correction terms. We apply both to the calculation of the simplest one-particle canonical partition functions for the translational, vibrational and rotational degrees of freedom. The more elaborate, systematic calculation of the correction terms is suitable for motivating the students to explore the possibility of using available computer algebra software that enable one to avoid long and tedious manipulation of algebraic equations.
Lee, S. J.; Mekjian, A. Z.
2004-01-01
Various phenomenological models of particle multiplicity distributions are discussed using a general form of a unified model which is based on the grand canonical partition function and Feynman's path integral approach to statistical processes. These models can be written as special cases of a more general distribution which has three control parameters which are a, x, z. The relation to these parameters to various physical quantities are discussed. A connection of the parameter a with Fisher's critical exponent τ is developed. Using this grand canonical approach, moments, cumulants and combinants are discussed and a physical interpretation of the combinants are given and their behavior connected to the critical exponent τ. Various physical phenomena such as hierarchical structure, void scaling relations, Koba-Nielson-Olesen or KNO scaling features, clan variables, and branching laws are shown in terms of this general approach. Several of these features which were previously developed in terms of the negative binomial distribution are found to be more general. Both hierarchical structure and void scaling relations depend on the Fisher exponent τ. Applications of our approach to the charged particle multiplicity distribution in jets of L3 and H1 data are given.
International Nuclear Information System (INIS)
Various phenomenological models of particle multiplicity distributions are discussed using a general form of a unified model which is based on the grand canonical partition function and Feynman's path integral approach to statistical processes. These models can be written as special cases of a more general distribution which has three control parameters which are a,x,z. The relation to these parameters to various physical quantities are discussed. A connection of the parameter a with Fisher's critical exponent τ is developed. Using this grand canonical approach, moments, cumulants and combinants are discussed and a physical interpretation of the combinants are given and their behavior connected to the critical exponent τ. Various physical phenomena such as hierarchical structure, void scaling relations, Koba-Nielson-Olesen or KNO scaling features, clan variables, and branching laws are shown in terms of this general approach. Several of these features which were previously developed in terms of the negative binomial distribution are found to be more general. Both hierarchical structure and void scaling relations depend on the Fisher exponent τ. Applications of our approach to the charged particle multiplicity distribution in jets of L3 and H1 data are given
Brambilla, M; Ugoccioni, R
2006-01-01
Theorems on zeros of the truncated generating function in the complex plane are reviewed. When examined in the framework of a statistical model of high energy collisions based on the negative binomial (Pascal) multiplicity distribution, these results lead to maps of zeros of the grand canonical partition function which allow us to interpret in a novel way different classes of events in pp collisions at LHC c.m. energies.
Brambilla, M.; Giovannini, A.; Ugoccioni, R.
2006-06-01
Theorems on zeros of the truncated generating function in the complex plane are reviewed. When examined in the framework of a statistical model of high energy collisions based on the negative binomial (Pascal) multiplicity distribution, these results lead to maps of zeros of the grand canonical partition function which allow us to interpret in a novel way different classes of events in pp collisions at LHC c.m. energies.
Brambilla, M.; Giovannini, A.; Ugoccioni, R.
2005-01-01
Theorems on zeroes of the truncated generating function in the complex plane are reviewed. When examined in the framework of a statistical model of high energy collisions based on the negative binomial (Pascal) multiplicity distribution, these results lead to maps of zeroes of the grand canonical partition function which allow to interpret in a novel way different classes of events in pp collisions at LHC c.m. energies.
Lee, S J
2002-01-01
Various phenomenological models of particle multiplicity distributions are discussed using a general form of the grand canonical partition function. These phenomenological models include a wide range of varied processes such as coherent emission or Poisson processes, chaotic emission resulting in a negative binomial distribution, combinations of coherent and chaotic processes called signal/noise distributions, and models based on field emission from Lorentzian line shapes leading to Lorentz/Catalan distributions. These specific cases can be written as special cases of a more general distribution. Using this grand canonical approach moments and cumulants, combinants, hierarchical structure, void scaling relations, KNO scaling features, clan variables and branching laws associated with stochastic or ancestral variables are discussed. It is shown that just looking at the mean and fluctuation of data is not enough to distinguish these distributions or the underlying mechanism. A generalization of the Poisson tran...
Hryniv, R O
2001-01-01
We study the self-avoiding polygons (SAP) connecting the vertical and the horizontal semi-axes of the positive quadrant of $\\mathbb{Z}^2$. For a fixed $\\beta>0$, assign to each such polygon $\\omega$ the weight $\\exp\\{-\\beta|\\omega|\\}$, $|\\omega|$ denoting the length of $\\omega$, and consider the sum $Z_{Q,+}$ of these weights for all SAP enclosing area $Q>0$. We study the statistical properties of such SAP and, in particular, derive the exact asymptotics for the partition function $Z_{Q,+}$ as $Q\\to\\infty$. The results are valid for any $\\beta >\\beta_c$, $\\beta_c$ being the critical value for the 2D self-avoiding walks.
Lee, S. J.; Mekjian, A. Z.
2003-01-01
Various phenomenological models of particle multiplicity distributions are discussed using a general form of a unified model which is based on the grand canonical partition function and Feynman's path integral approach to statistical processes. These models can be written as special cases of a more general distribution which has three control parameters which are $a$, $x$, $z$. The relation to these parameters to various physical quantities are discussed. A connection of the parameter $a$ wit...
Lee, S J
2004-01-01
Various phenomenological models of particle multiplicity distributions are discussed using a general form of a unified model which is based on the grand canonical partition function and Feynman's path integral approach to statistical processes. These models can be written as special cases of a more general distribution which has three control parameters which are $a$, $x$, $z$. The relation to these parameters to various physical quantities are discussed. A connection of the parameter $a$ with Fisher's critical exponent $\\tau$ is developed. Using this grand canonical approach, moments, cumulants and combinants are discussed and a physical interpretation of the combinants are given and their behavior connected to the critical exponent $\\tau$. Various physical phenomena such as hierarchical structure, void scaling relations, KNO scaling features, clan variables, and branching laws are shown in terms of this general approach. Several of these features which were previously developed in terms of the negative bino...
Rocha, Julio; Mol, Lucas; Costa, Bismarck
2015-03-01
In this work we show that the canonical partition function zeros, the Fisher zeros, can be used to uniquely characterize a transition as being in the Berezinskii-Kosterlitz-Thouless (BKT) class of universality. By studying the zeros map for the 2D XY model we found that its internal border coalesces into the real positive axis in a finite region corresponding to temperatures smaller than the BKT transition temperature. This behavior is consistent with the predicted existence of a line of critical points below the transition temperature, allowing one to distinguish the BKT class of universality from other ones. This work was partially supported by CNPq and Fapemig, Brazilian Agencies.
Kellerstein, M; Verbaarschot, J J M
2016-01-01
The behavior of quenched Dirac spectra of two-dimensional lattice QCD is consistent with spontaneous chiral symmetry breaking which is forbidden according to the Coleman-Mermin-Wagner theorem. One possible resolution of this paradox is that, because of the bosonic determinant in the partially quenched partition function, the conditions of this theorem are violated allowing for spontaneous symmetry breaking in two dimensions or less. This goes back to work by Niedermaier and Seiler on nonamenable symmetries of the hyperbolic spin chain and earlier work by two of the auhtors on bosonic partition functions at nonzero chemical potential. In this talk we discuss chiral symmetry breaking for the bosonic partition function of QCD at nonzero isospin chemical potential and a bosonic random matrix theory at imaginary chemical potential and compare the results with the fermionic counterpart. In both cases the chiral symmetry group of the bosonic partition function is noncompact.
Functional Multiple-Set Canonical Correlation Analysis
Hwang, Heungsun; Jung, Kwanghee; Takane, Yoshio; Woodward, Todd S.
2012-01-01
We propose functional multiple-set canonical correlation analysis for exploring associations among multiple sets of functions. The proposed method includes functional canonical correlation analysis as a special case when only two sets of functions are considered. As in classical multiple-set canonical correlation analysis, computationally, the…
Partition density functional theory
Nafziger, Jonathan
Partition density functional theory (PDFT) is a method for dividing a molecular electronic structure calculation into fragment calculations. The molecular density and energy corresponding to Kohn Sham density-functional theory (KS-DFT) may be exactly recovered from these fragments. Each fragment acts as an isolated system except for the influence of a global one-body 'partition' potential which deforms the fragment densities. In this work, the developments of PDFT are put into the context of other fragment-based density functional methods. We developed three numerical implementations of PDFT: One within the NWChem computational chemistry package using basis sets, and the other two developed from scratch using real-space grids. It is shown that all three of these programs can exactly reproduce a KS-DFT calculation via fragment calculations. The first of our in-house codes handles non-interacting electrons in arbitrary one-dimensional potentials with any number of fragments. This code is used to explore how the exact partition potential changes for different partitionings of the same system and also to study features which determine which systems yield non-integer PDFT occupations and which systems are locked into integer PDFT occupations. The second in-house code, CADMium, performs real-space calculations of diatomic molecules. Features of the exact partition potential are studied for a variety of cases and an analytical formula determining singularities in the partition potential is derived. We introduce an approximation for the non-additive kinetic energy and show how this quantity can be computed exactly. Finally a PDFT functional is developed to address the issues of static correlation and delocalization errors in approximations within DFT. The functional is applied to the dissociation of H2 + and H2.
Matrix string partition function
Kostov, Ivan K; Kostov, Ivan K.; Vanhove, Pierre
1998-01-01
We evaluate quasiclassically the Ramond partition function of Euclidean D=10 U(N) super Yang-Mills theory reduced to a two-dimensional torus. The result can be interpreted in terms of free strings wrapping the space-time torus, as expected from the point of view of Matrix string theory. We demonstrate that, when extrapolated to the ultraviolet limit (small area of the torus), the quasiclassical expressions reproduce exactly the recently obtained expression for the partition of the completely reduced SYM theory, including the overall numerical factor. This is an evidence that our quasiclassical calculation might be exact.
Generalised twisted partition functions
Petkova, V B
2001-01-01
We consider the set of partition functions that result from the insertion of twist operators compatible with conformal invariance in a given 2D Conformal Field Theory (CFT). A consistency equation, which gives a classification of twists, is written and solved in particular cases. This generalises old results on twisted torus boundary conditions, gives a physical interpretation of Ocneanu's algebraic construction, and might offer a new route to the study of properties of CFT.
Functional linear regression via canonical analysis
He, Guozhong; Wang, Jane-Ling; Yang, Wenjing; 10.3150/09-BEJ228
2011-01-01
We study regression models for the situation where both dependent and independent variables are square-integrable stochastic processes. Questions concerning the definition and existence of the corresponding functional linear regression models and some basic properties are explored for this situation. We derive a representation of the regression parameter function in terms of the canonical components of the processes involved. This representation establishes a connection between functional regression and functional canonical analysis and suggests alternative approaches for the implementation of functional linear regression analysis. A specific procedure for the estimation of the regression parameter function using canonical expansions is proposed and compared with an established functional principal component regression approach. As an example of an application, we present an analysis of mortality data for cohorts of medflies, obtained in experimental studies of aging and longevity.
Canonic form of linear quaternion functions
Sangwine, Stephen J.
2008-01-01
The general linear quaternion function of degree one is a sum of terms with quaternion coefficients on the left and right. The paper considers the canonic form of such a function, and builds on the recent work of Todd Ell, who has shown that any such function may be represented using at most four quaternion coefficients. In this paper, a new and simple method is presented for obtaining these coefficients numerically using a matrix approach which also gives an alternative proof of the canonic ...
Partial domain wall partition functions
Foda, O.; Wheeler, M.
2012-01-01
We consider six-vertex model configurations on an n-by-N lattice, n =< N, that satisfy a variation on domain wall boundary conditions that we define and call "partial domain wall boundary conditions". We obtain two expressions for the corresponding "partial domain wall partition function", as an (N-by-N)-determinant and as an (n-by-n)-determinant. The latter was first obtained by I Kostov. We show that the two determinants are equal, as expected from the fact that they are partition functions...
On higher spin partition functions
Beccaria, M
2015-01-01
We observe that the partition function of the set of all free massless higher spins s=0,1,2,3,... in flat space is equal to one: the ghost determinants cancel against the "physical" ones or, equivalently, the (regularized) total number of degrees of freedom vanishes. This reflects large underlying gauge symmetry and suggests analogy with supersymmetric or topological theory. The Z=1 property extends also to the AdS background, i.e. the 1-loop vacuum partition function of Vasiliev theory is equal to 1 (assuming a particular regularization of the sum over spins); this was noticed earlier as a consistency requirement for the vectorial AdS/CFT duality. We find that Z=1 is also true in the conformal higher spin theory (with higher-derivative d^{2s} kinetic terms) expanded near flat or conformally flat S^4 background. We also consider the partition function of free conformal theory of symmetric traceless rank s tensor field which has 2-derivative kinetic term but only scalar gauge invariance in flat space. This non...
On higher spin partition functions
Beccaria, Matteo; Tseytlin, Arkady A.
2015-07-01
We observe that the partition function of the set of all free massless higher spins s = 0, 1, 2, 3,... in flat space is equal to one: the ghost determinants cancel against the ‘physical’ ones or, equivalently, the (regularized) total number of degrees of freedom vanishes. This reflects large underlying gauge symmetry and suggests analogy with supersymmetric or topological theory. The Z = 1 property extends also to the AdS background, i.e. the 1-loop vacuum partition function of Vasiliev theory is equal to 1 (assuming a particular regularization of the sum over spins); this was noticed earlier as a consistency requirement for the vectorial AdS/CFT duality. We find that Z = 1 is true also in the conformal higher spin theory (with higher-derivative {\\partial }2s kinetic terms) expanded near flat or conformally flat S4 background. We also consider the partition function of free conformal theory of symmetric traceless rank s tensor field which has 2-derivative kinetic term but only scalar gauge invariance in flat 4d space. This non-unitary theory has Weyl-invariant action in curved background and it corresponds to ‘partially massless’ field in AdS5. We discuss in detail the special case of s = 2 (or ‘conformal graviton’), compute the corresponding conformal anomaly coefficients and compare them with previously found expressions for generic representations of conformal group in 4 dimensions.
The Functional Determinant and the Partition Function in Geometric Flows
Lin, Christopher
2013-01-01
We propose the use of the functional determinant of geometric operators in constructing an entropy functional associated to geometric flows. Our approach is based on the direct computation of the partition function, with a well-defined set of microstates and macrostates in the canonical ensemble. The approach is motivated by a fundamental enigma in Perelman's derivation of his famous $\\mathcal{W}$-entropy. The defining feature of our entropy is that the energy of each microstate in the partition function is invariant along the associated geometric flow - a clue that could be inferred from Perelman's work. Moreover, the monotonicity of our entropy along the associated geometric flow is then a natural result in the statistical mechanics framework. While we will not argue in a completely rigorous manner, we will use the formalism to derive an explicit formula for an entropy associated to conformal flows on a closed surface based on the Polyakov formula for the determinant of the Laplacian. We also discuss possib...
Approximate path integral methods for partition functions
International Nuclear Information System (INIS)
We review several approximate methods for evaluating quantum mechanical partition functions with the goal of obtaining a method that is easy to implement for multidimensional systems but accurately incorporates quantum mechanical corrections to classical partition functions. A particularly promising method is one based upon an approximation to the path integral expression of the partition function. In this method, the partition-function expression has the ease of evaluation of a classical partition function, and quantum mechanical effects are included by a weight function. Anharmonicity is included exactly in the classical Boltzmann average and local quadratic expansions around the centroid of the quantum paths yield a simple analytic form for the quantum weight function. We discuss the relationship between this expression and previous approximate methods and present numerical comparisons for model one-dimensional potentials and for accurate three-dimensional vibrational force fields for H2O and SO2
Desgranges, Caroline; Delhommelle, Jerome
2016-03-28
We extend Expanded Wang-Landau (EWL) simulations beyond classical systems and develop the EWL method for systems modeled with a tight-binding Hamiltonian. We then apply the method to determine the partition function and thus all thermodynamic properties, including the Gibbs free energy and entropy, of the fluid phases of Si. We compare the results from quantum many-body (QMB) tight binding models, which explicitly calculate the overlap between the atomic orbitals of neighboring atoms, to those obtained with classical many-body (CMB) force fields, which allow to recover the tetrahedral organization in condensed phases of Si through, e.g., a repulsive 3-body term that favors the ideal tetrahedral angle. Along the vapor-liquid coexistence, between 3000 K and 6000 K, the densities for the two coexisting phases are found to vary significantly (by 5 orders of magnitude for the vapor and by up to 25% for the liquid) and to provide a stringent test of the models. Transitions from vapor to liquid are predicted to occur for chemical potentials that are 10%-15% higher for CMB models than for QMB models, and a ranking of the force fields is provided by comparing the predictions for the vapor pressure to the experimental data. QMB models also reveal the formation of a gap in the electronic density of states of the coexisting liquid at high temperatures. Subjecting Si to a nanoscopic confinement has a dramatic effect on the phase diagram with, e.g. at 6000 K, a decrease in liquid densities by about 50% for both CMB and QMB models and an increase in vapor densities between 90% (CMB) and 170% (QMB). The results presented here provide a full picture of the impact of the strategy (CMB or QMB) chosen to model many-body effects on the thermodynamic properties of the fluid phases of Si. PMID:27036464
Desgranges, Caroline; Delhommelle, Jerome
2016-03-01
We extend Expanded Wang-Landau (EWL) simulations beyond classical systems and develop the EWL method for systems modeled with a tight-binding Hamiltonian. We then apply the method to determine the partition function and thus all thermodynamic properties, including the Gibbs free energy and entropy, of the fluid phases of Si. We compare the results from quantum many-body (QMB) tight binding models, which explicitly calculate the overlap between the atomic orbitals of neighboring atoms, to those obtained with classical many-body (CMB) force fields, which allow to recover the tetrahedral organization in condensed phases of Si through, e.g., a repulsive 3-body term that favors the ideal tetrahedral angle. Along the vapor-liquid coexistence, between 3000 K and 6000 K, the densities for the two coexisting phases are found to vary significantly (by 5 orders of magnitude for the vapor and by up to 25% for the liquid) and to provide a stringent test of the models. Transitions from vapor to liquid are predicted to occur for chemical potentials that are 10%-15% higher for CMB models than for QMB models, and a ranking of the force fields is provided by comparing the predictions for the vapor pressure to the experimental data. QMB models also reveal the formation of a gap in the electronic density of states of the coexisting liquid at high temperatures. Subjecting Si to a nanoscopic confinement has a dramatic effect on the phase diagram with, e.g. at 6000 K, a decrease in liquid densities by about 50% for both CMB and QMB models and an increase in vapor densities between 90% (CMB) and 170% (QMB). The results presented here provide a full picture of the impact of the strategy (CMB or QMB) chosen to model many-body effects on the thermodynamic properties of the fluid phases of Si.
Partial domain wall partition functions
Foda, O
2012-01-01
We consider six-vertex model configurations on a rectangular lattice with n (N) horizontal (vertical) lines, and "partial domain wall boundary conditions" defined as 1. all 2n arrows on the left and right boundaries point inwards, 2. n_u (n_l) arrows on the upper (lower) boundary, such that n_u + n_l = N - n, also point inwards, 3. all remaining n+N arrows on the upper and lower boundaries point outwards, and 4. all spin configurations on the upper and lower boundaries are summed over. To generate (n-by-N) "partial domain wall configurations", one can start from A. (N-by-N) configurations with domain wall boundary conditions and delete n_u (n_l) upper (lower) horizontal lines, or B. (2n-by-N) configurations that represent the scalar product of an n-magnon Bethe eigenstate and an n-magnon generic state on an N-site spin-1/2 chain, and delete the n lines that represent the Bethe eigenstate. The corresponding "partial domain wall partition function" is computed in construction {A} ({B}) as an N-by-N (n-by-n) det...
Canonical Duality Theory for Solving Minimization Problem of Rosenbrock Function
Gao, David Y.; Zhang, Jiapu
2011-01-01
This paper presents a canonical duality theory for solving nonconvex minimization problem of Rosenbrock function. Extensive numerical results show that this benchmark test problem can be solved precisely and efficiently to obtain global optimal solutions.
Perturbative partition function for squashed S^5
Imamura, Yosuke
2012-01-01
We compute the index of 6d N=(1,0) theories on S^5xR containing vector and hypermultiplets. We only consider the perturbative sector without instantons. By compactifying R to S^1 with a twisted boundary condition and taking the small radius limit, we derive the perturbative partition function on a squashed S^5. The 1-loop partition function is represented in a simple form with the triple sine function.
Grand partition function of hadronic bremsstrahlung
International Nuclear Information System (INIS)
The grand partition function of hadronic bremsstrahlung is obtained using saddle-point procedures. Several levels of approximation are considered. The results are qualitatively consistent with earlier simple approximations
Statistical thermodynamics in relativistic particle and ion physics: Canonical or grand canonical
International Nuclear Information System (INIS)
We consider relativistic statistical thermodynamics of an ideal Boltzmann gas consisting of the particles K, Λ, A, Σ and their antiparticles. Baryon number (B) and strangeness (S) are conserved. While any relativistic gas is necessarily grand canonical with respect to particle numbers, conservation laws can be treated canonically or grand canonically. We construct the partition function for canonical BxS conservation and compare it with the grand canonical one. It is found that the grand canonical partition function is equivalent to a large B approximation of the canonical one. The relative difference between canonical and grand canonical quantities seems to decrease like const/B (two numerical examples) and from this a simple thumb rule for computing canonical quantities from grand canonical ones is guessed. For precise calculations, an integral representation is given. (orig.)
Partition Function of Interacting Calorons Ensemble
Deldar, Sedigheh
2015-01-01
We present a method for computing the partition function of a caloron ensemble taking into account the interaction of calorons. We focus on caloron-Dirac string interaction and show that the metric that Diakonov and Petrov offered works well in the limit where this interaction occurs. We suggest computing the correlation function of two polyakov loops by applying Ewald's method.
Partition function of interacting calorons ensemble
Deldar, S.; Kiamari, M.
2016-01-01
We present a method for computing the partition function of a caloron ensemble taking into account the interaction of calorons. We focus on caloron-Dirac string interaction and show that the metric that Diakonov and Petrov offered, works well in the limit where this interaction occurs. We suggest computing the correlation function of two polyakov loops by applying Ewald's method.
Domain wall partition functions and KP
International Nuclear Information System (INIS)
We observe that the partition function of the six-vertex model on a finite square lattice with domain wall boundary conditions is (a restriction of) a KP τ function and express it as an expectation value of charged free fermions (up to an overall normalization)
Domain wall partition functions and KP
Foda, O; Zuparic, M
2009-01-01
We observe that the partition function of the six vertex model on a finite square lattice with domain wall boundary conditions is (a restriction of) a KP tau function and express it as an expectation value of charged free fermions (up to an overall normalization).
Partition functions and graphs: A combinatorial approach
Solomon, A I; Duchamp, G; Horzela, A; Penson, K A; Solomon, Allan I.; Blasiak, Pawel; Duchamp, Gerard; Horzela, Andrzej; Penson, Karol A.
2004-01-01
Although symmetry methods and analysis are a necessary ingredient in every physicist's toolkit, rather less use has been made of combinatorial methods. One exception is in the realm of Statistical Physics, where the calculation of the partition function, for example, is essentially a combinatorial problem. In this talk we shall show that one approach is via the normal ordering of the second quantized operators appearing in the partition function. This in turn leads to a combinatorial graphical description, giving essentially Feynman-type graphs associated with the theory. We illustrate this methodology by the explicit calculation of two model examples, the free boson gas and a superfluid boson model. We show how the calculation of partition functions can be facilitated by knowledge of the combinatorics of the boson normal ordering problem; this naturally gives rise to the Bell numbers of combinatorics. The associated graphical representation of these numbers gives a perturbation expansion in terms of a sequen...
Twist-4 effects in electroproduction: Canonical operators and coefficient functions
International Nuclear Information System (INIS)
The interpretation of observed scaling violations in leptoproduction is complicated by the possible presence of significant higher-twist effects. We refine the machinery of the operator-product expansion sufficiently for a study of twist-4 effects. In particular, we introduce and review the advantages of a special, ''canonical'' basis. We demonstrate that the canonical basis is adequate for the necessary twist-4 perturbative calculations, and calculate the operator's tree-level coefficient functions in electroproduction. Our results establish a framework within which careful analysis of more accurate data can provide information regarding correlations among the constituents of the proton
Derivation of Mayer Series from Canonical Ensemble
Xian-Zhi, Wang
2016-02-01
Mayer derived the Mayer series from both the canonical ensemble and the grand canonical ensemble by use of the cluster expansion method. In 2002, we conjectured a recursion formula of the canonical partition function of a fluid (X.Z. Wang, Phys. Rev. E 66 (2002) 056102). In this paper we give a proof for this formula by developing an appropriate expansion of the integrand of the canonical partition function. We further derive the Mayer series solely from the canonical ensemble by use of this recursion formula.
Indefinite theta functions and black hole partition functions
International Nuclear Information System (INIS)
We explore various aspects of supersymmetric black hole partition functions in four-dimensional toroidally compactified heterotic string theory. These functions suffer from divergences owing to the hyperbolic nature of the charge lattice in this theory, which prevents them from having well-defined modular transformation properties. In order to rectify this, we regularize these functions by converting the divergent series into indefinite theta functions, thereby obtaining fully regulated single-centered black hole partitions functions
Indefinite theta functions and black hole partition functions
Energy Technology Data Exchange (ETDEWEB)
Cardoso, Gabriel Lopes; Cirafici, Michele [Center for Mathematical Analysis, Geometry, and Dynamical Systems,Departamento de Matemática and LARSyS, Instituto Superior Técnico,1049-001 Lisboa (Portugal); Jorge, Rogério [Instituto Superior Técnico,1049-001 Lisboa (Portugal); Nampuri, Suresh [Laboratoire de Physique Théorique, École Normale Supérieure,24 rue Lhomond, 75231 Paris Cedex 05 (France)
2014-02-05
We explore various aspects of supersymmetric black hole partition functions in four-dimensional toroidally compactified heterotic string theory. These functions suffer from divergences owing to the hyperbolic nature of the charge lattice in this theory, which prevents them from having well-defined modular transformation properties. In order to rectify this, we regularize these functions by converting the divergent series into indefinite theta functions, thereby obtaining fully regulated single-centered black hole partitions functions.
Virasoro constraint for Nekrasov instanton partition function
Kanno, Shoichi; Zhang, Hong
2012-01-01
We show that Nekrasov instanton partition function for SU(N) gauge theories satisfies recursion relations in the form of U(1)+Virasoro constraints when {\\beta} = 1. The constraints give a direct support for AGT conjecture for general quiver gauge theories.
Some reference formulas for the generating functions of canonical transformations
Anselmi, Damiano
2016-02-01
We study some properties of the canonical transformations in classical mechanics and quantum field theory and give a number of practical formulas concerning their generating functions. First, we give a diagrammatic formula for the perturbative expansion of the composition law around the identity map. Then we propose a standard way to express the generating function of a canonical transformation by means of a certain "componential" map, which obeys the Baker-Campbell-Hausdorff formula. We derive the diagrammatic interpretation of the componential map, work out its relation with the solution of the Hamilton-Jacobi equation and derive its time-ordered version. Finally, we generalize the results to the Batalin-Vilkovisky formalism, where the conjugate variables may have both bosonic and fermionic statistics, and describe applications to quantum field theory.
Some reference formulas for the generating functions of canonical transformations
Anselmi, Damiano
2015-01-01
We study some properties of the canonical transformations in classical mechanics and quantum field theory and give a number of practical formulas concerning their generating functions. First, we give a diagrammatic formula for the perturbative expansion of the composition law around the identity map. Then, we propose a standard way to express the generating function of a canonical transformation by means of a certain "componential" map, which obeys the Baker-Campbell-Hausdorff formula. We derive the diagrammatic interpretation of the componential map, work out its relation with the solution of the Hamilton-Jacobi equation and derive its time-ordered version. Finally, we generalize the results to the Batalin-Vilkovisky formalism, where the conjugate variables may have both bosonic and fermionic statistics, and describe applications to quantum field theory.
Some reference formulas for the generating functions of canonical transformations
Energy Technology Data Exchange (ETDEWEB)
Anselmi, Damiano [Universita di Pisa, Dipartimento di Fisica ' ' Enrico Fermi' ' , Pisa (Italy); INFN, Sezione di Pisa, Pisa (Italy)
2016-02-15
We study some properties of the canonical transformations in classical mechanics and quantum field theory and give a number of practical formulas concerning their generating functions. First, we give a diagrammatic formula for the perturbative expansion of the composition law around the identity map. Then we propose a standard way to express the generating function of a canonical transformation by means of a certain ''componential'' map, which obeys the Baker-Campbell-Hausdorff formula. We derive the diagrammatic interpretation of the componential map, work out its relation with the solution of the Hamilton-Jacobi equation and derive its time-ordered version. Finally, we generalize the results to the Batalin-Vilkovisky formalism, where the conjugate variables may have both bosonic and fermionic statistics, and describe applications to quantum field theory. (orig.)
Some reference formulas for the generating functions of canonical transformations
International Nuclear Information System (INIS)
We study some properties of the canonical transformations in classical mechanics and quantum field theory and give a number of practical formulas concerning their generating functions. First, we give a diagrammatic formula for the perturbative expansion of the composition law around the identity map. Then we propose a standard way to express the generating function of a canonical transformation by means of a certain ''componential'' map, which obeys the Baker-Campbell-Hausdorff formula. We derive the diagrammatic interpretation of the componential map, work out its relation with the solution of the Hamilton-Jacobi equation and derive its time-ordered version. Finally, we generalize the results to the Batalin-Vilkovisky formalism, where the conjugate variables may have both bosonic and fermionic statistics, and describe applications to quantum field theory. (orig.)
A canonical correlation analysis of intelligence and executive functioning.
Davis, Andrew S; Pierson, Eric E; Finch, W Holmes
2011-01-01
Executive functioning is one of the most researched and debated topics in neuropsychology. Although neuropsychologists routinely consider executive functioning and intelligence in their assessment process, more information is needed regarding the relationship between these constructs. This study reports the results of a canonical correlation study between the most widely used measure of adult intelligence, the Wechsler Adult Intelligence Scale, 3rd edition (WAIS-III; Wechsler, 1997), and the Delis-Kaplan Executive Function System (D-KEFS; Delis, Kaplan, & Kramer, 2001). The results suggest that, despite considerable shared variability, the measures of executive functioning maintain unique variance that is not encapsulated in the construct of global intelligence. PMID:21390902
Sifting Function Partition for the Goldbach Problem
Song, Fu-Gao
2008-01-01
All sieve methods for the Goldbach problem sift out all the composite numbers; even though, strictly speaking, it is not necessary to do so and which is, in general, very difficult. Some new methods introduced in this paper show that the Goldbach problem can be solved under sifting out only some composite numbers. In fact, in order to prove the Goldbach conjecture, it is only necessary to show that there are prime numbers left in the residual integers after the initial sifting! This idea can be implemented by using one of the three methods called sifting function partition by integer sort, sifting function partition by intervals and comparative sieve method, respectively. These are feasible methods for solving both the Goldbach problem and the problem of twin primes. An added bonus of the above methods is the elimination of the indeterminacy of the sifting functions brought about by their upper and lower bounds.
Supersymmetric partition functions on Riemann surfaces
Benini, Francesco
2016-01-01
We present a compact formula for the supersymmetric partition function of 2d N=(2,2), 3d N=2 and 4d N=1 gauge theories on $\\Sigma_g \\times T^n$ with partial topological twist on $\\Sigma_g$, where $\\Sigma_g$ is a Riemann surface of arbitrary genus and $T^n$ is a torus with n=0,1,2, respectively. In 2d we also include certain local operator insertions, and in 3d we include Wilson line operator insertions along $S^1$. For genus g=1, the formula computes the Witten index. We present a few simple Abelian and non-Abelian examples, including new tests of non-perturbative dualities. We also show that the large N partition function of ABJM theory on $\\Sigma_g \\times S^1$ reproduces the Bekenstein-Hawking entropy of BPS black holes in AdS4 whose horizon has $\\Sigma_g$ topology.
On partition function in Astronomy \\& Astrophysics
Sharma, M K; Chandra, Suresh
2015-01-01
In order to analyze spectrum from the interstellar medium (ISM), spectrum of the molecule of interest is recorded in a laboratory, and accurate rotational and centrifugal distortion constants are derived. By using these constants, one can calculate accurate partition function. However, in the same paper, where these constants are derived, the partition function is calculated by using a semi-empirical expression. We have looked into the details of this semi-empirical expression and compared the values, obtained from it, with the accurate ones. As an example, we have considered the case of Methanimine (CH$_2$NH) which is detected in a number of cosmic objects. It is found that for the kinetic temperature $T > 120$ K, the semi-empirical expression gives large value as compared to the accurate one. The deviation becomes about 25\\% larger than the accurate one at the kinetic temperature of 400 K.
The geometry of supersymmetric partition functions
Cyril Closset; Dumitrescu, Thomas T.; Guido Festuccia; Zohar Komargodski
2014-01-01
We consider supersymmetric field theories on compact manifolds $ \\mathcal{M} $ and obtain constraints on the parameter dependence of their partition functions $ {Z_{\\mathcal{M}}} $ . Our primary focus is the dependence of $ {Z_{\\mathcal{M}}} $ on the geometry of $ \\mathcal{M} $ , as well as background gauge fields that couple to continuous flavor symmetries. For $ \\mathcal{N} $ = 1 theories with a U(1) R symmetry in four dimensions, $ \\mathcal{M} $ must be a complex manifold with a Hermitian ...
Superfluid Kubo Formulas from Partition Function
Chapman, Shira; Oz, Yaron
2014-01-01
Linear response theory relates hydrodynamic transport coefficients to equilibrium retarded correlation functions of the stress-energy tensor and global symmetry currents in terms of Kubo formulas. Some of these transport coefficients are non-dissipative and affect the fluid dynamics at equilibrium. We present an algebraic framework for deriving Kubo formulas for such thermal transport coefficients by using the equilibrium partition function. We use the framework to derive Kubo formulas for all such transport coefficients of superfluids, as well as to rederive Kubo formulas for various normal fluid systems.
Denominator function for canonical SU(3) tensor operators
International Nuclear Information System (INIS)
The definition of a canonical unit SU(3) tensor operator is given in terms of its characteristic null space as determined by group-theoretic properties of the intertwining number. This definition is shown to imply the canonical splitting conditions used in earlier work for the explicit and unique (up to +- phases) construction of all SU(3) WCG coefficients (Wigner--Clebsch--Gordan). Using this construction, an explicit SU(3)-invariant denominator function characterizing completely the canonically defined WCG coefficients is obtained. It is shown that this denominator function (squared) is a product of linear factors which may be obtained explicitly from the characteristic null space times a ratio of polynomials. These polynomials, denoted G/sup t//sub q/, are defined over three (shift) parameters and three barycentric coordinates. The properties of these polynomials (hence, of the corresponding invariant denominator function) are developed in detail: These include a derivation of their degree, symmetries, and zeros. The symmetries are those induced on the shift parameters and barycentric coordinates by the transformations of a 3 x 3 array under row interchange, column interchange, and transposition (the group of 72 operations leaving a 3 x 3 determinant invariant). Remarkably, the zeros of the general G/sup t//sub q/ polynomial are in position and multiplicity exactly those of the SU(3) weight space associated with irreducible representation [q-1,t-1,0]. The results obtained are an essential step in the derivation of a fully explicit and comprehensible algebraic expression for all SU(3) WCG coefficients
Surface defects and instanton partition functions
Gaiotto, Davide
2014-01-01
We study the superconformal index of five-dimensional SCFTs and the sphere partition function of four-dimensional gauge theories with eight supercharges in the presence of co-dimension two half-BPS defects. We derive a prescription which is valid for defects which can be given a "vortex construction", i.e. can be defined by RG flow from vortex configurations in a larger theory. We test the prescription against known results and expected dualities. We employ our prescription to develop a general computational strategy for defects defined by coupling the bulk degrees of freedom to a Gauged Linear Sigma Model living in co-dimension two.
Partition functions, duality and the tube metric
International Nuclear Information System (INIS)
The partition function of type IIA and B strings on R6 x K3, in the T4/Z2 orbifold limit, is explicitly computed as a modular invariant sum over spin structures required by perturbative unitarity in order to extend the analysis to include type II strings on R6 x W4, where W4 is associated with the tube metric conformal field theory, given by the degrees of freedom transverse to the Neveu-Schwarz fivebrane solution. This generates partition functions and perturbative spectra of string theories in six space-time dimensions, associated with the modular invariants of the level-k affine SU(2) Kac-Moody algebra. These theories provide a conformal field theory (i.e. perturbative) probe of non-perturbative (fivebrane) vacua. We contrast them with theories whose N=(4,4) sigma-model action contains nH=k+2 hypermultiplets as well as vector supermultiplets, and where k is the level just mentioned. In Appendix B we also give a D=6, N=(1,1) 'free fermion' string model which has a different moduli space of vacua from the 81-parameter space relevant to the above examples. (orig.)
Partition function for a singular background
International Nuclear Information System (INIS)
We present a method for evaluating the partition function in a varying external field. Specifically, we look at the case of a non-interacting, charged, massive scalar field at finite temperature with an associated chemical potential in the background of a delta-function potential. Whilst we present a general method, valid at all temperatures, we only give the result for the leading order term in the high temperature limit. Although the derivative expansion breaks down for inhomogeneous backgrounds we are able to obtain the high temperature expansion, as well as an analytic expression for the zero point energy, by way of a different approximation scheme, which we call the local Born approximation (LBA)
Modular properties of full 5D SYM partition function
Qiu, Jian; Tizzano, Luigi; Winding, Jacob; Zabzine, Maxim
2016-03-01
We study properties of the full partition function for the U(1) 5D N = {2}^{ast } gauge theory with adjoint hypermultiplet of mass M . This theory is ultimately related to abelian 6D (2,0) theory. We construct the full non-perturbative partition function on toric Sasaki-Einstein manifolds by gluing flat copies of the Nekrasov partition function and we express the full partition function in terms of the generalized double elliptic gamma function G 2 C associated with a certain moment map cone C. The answer exhibits a curious SL(4 , ℤ) modular property. Finally, we propose a set of rules to construct the partition function that resembles the calculation of 5d supersymmetric partition function with the insert ion of defects of various co-dimensions.
S^3/Z_n partition function and dualities
Imamura, Yosuke
2012-01-01
We investigate S^3/Z_n partition function of N = 2 supersymmetric gauge theories. A gauge theory on the orbifold has degenerate vacua specified by the holonomy. The partition function is obtained by summing up the contributions of saddle points with different holonomies. An appropriate choice of the phase of each contribution is essential to obtain the partition function. We determine the relative phases in the holonomy sum in a few examples by using duality to non-gauge theories. In the case of odd n the phase factors can be absorbed by modifying a single function appearing in the partition function.
Partition function of nearest neighbour Ising models: Some new insights
Indian Academy of Sciences (India)
G Nandhini; M V Sangaranarayanan
2009-09-01
The partition function for one-dimensional nearest neighbour Ising models is estimated by summing all the energy terms in the Hamiltonian for N sites. The algebraic expression for the partition function is then employed to deduce the eigenvalues of the basic 2 × 2 matrix and the corresponding Hermitian Toeplitz matrix is derived using the Discrete Fourier Transform. A new recurrence relation pertaining to the partition function for two-dimensional Ising models in zero magnetic field is also proposed.
Frady, E Paxon; Kapoor, Ashish; Horvitz, Eric; Kristan, William B
2016-08-01
Large-scale data collection efforts to map the brain are underway at multiple spatial and temporal scales, but all face fundamental problems posed by high-dimensional data and intersubject variability. Even seemingly simple problems, such as identifying a neuron/brain region across animals/subjects, become exponentially more difficult in high dimensions, such as recognizing dozens of neurons/brain regions simultaneously. We present a framework and tools for functional neurocartography-the large-scale mapping of neural activity during behavioral states. Using a voltage-sensitive dye (VSD), we imaged the multifunctional responses of hundreds of leech neurons during several behaviors to identify and functionally map homologous neurons. We extracted simple features from each of these behaviors and combined them with anatomical features to create a rich medium-dimensional feature space. This enabled us to use machine learning techniques and visualizations to characterize and account for intersubject variability, piece together a canonical atlas of neural activity, and identify two behavioral networks. We identified 39 neurons (18 pairs, 3 unpaired) as part of a canonical swim network and 17 neurons (8 pairs, 1 unpaired) involved in a partially overlapping preparatory network. All neurons in the preparatory network rapidly depolarized at the onsets of each behavior, suggesting that it is part of a dedicated rapid-response network. This network is likely mediated by the S cell, and we referenced VSD recordings to an activity atlas to identify multiple cells of interest simultaneously in real time for further experiments. We targeted and electrophysiologically verified several neurons in the swim network and further showed that the S cell is presynaptic to multiple neurons in the preparatory network. This study illustrates the basic framework to map neural activity in high dimensions with large-scale recordings and how to extract the rich information necessary to perform
On the canonical decomposition of generalized modular functions
Kohnen, Winfried
2010-01-01
The authors have conjectured (\\cite{KoM}) that if a normalized generalized modular function (GMF) $f$, defined on a congruence subgroup $\\Gamma$, has integral Fourier coefficients, then $f$ is classical in the sense that some power $f^m$ is a modular function on $\\Gamma$. A strengthened form of this conjecture was proved (loc cit) in case the divisor of $f$ is \\emph{empty}. In the present paper we study the canonical decomposition of a normalized parabolic GMF $f = f_1f_0$ into a product of normalized parabolic GMFs $f_1, f_0$ such that $f_1$ has \\emph{unitary character} and $f_0$ has \\emph{empty divisor}. We show that the strengthened form of the conjecture holds if the first "few" Fourier coefficients of $f_1$ are algebraic. We deduce proofs of several new cases of the conjecture, in particular if either $f_0=1$ or if the divisor of $f$ is concentrated at the cusps of $\\Gamma$.
Superconformal indices and partition functions for supersymmetric field theories
Energy Technology Data Exchange (ETDEWEB)
Gahramanov, I.B. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Humboldt-Universitaet, Berlin (Germany). Inst. fuer Physik; Vartanov, G.S. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)
2012-12-15
Recently there was a substantial progress in understanding of supersymmetric theories (in particular, their BPS spectrum) in space-times of different dimensions due to the exact computation of superconformal indices and partition functions using localization method. Here we discuss a connection of 4d superconformal indices and 3d partition functions using a particular example of supersymmetric theories with matter in antisymmetric representation.
N=4 superconformal characters and partition functions
International Nuclear Information System (INIS)
Character formulae for positive energy unitary representations of the N=4 superconformal group are obtained through use of reduced Verma modules and Weyl group symmetry. Expansions of these are given which determine the particular representations present and results such as dimensions of superconformal multiplets. By restriction of variables various 'blind' characters are also obtained. Limits, corresponding to reduction to particular subgroups, in the characters isolate contributions from particular subsets of multiplets and in many cases simplify the results considerably. As a special case, the index counting short and semi-short multiplets which do not form long multiplets found recently is shown to be related to particular cases of reduced characters. Partition functions of N=4 super-Yang-Mills are investigated. Through analysis of these, exact formulae are obtained for counting 12- and some 14-BPS operators in the free case. Similarly, partial results for the counting of semi-short operators are given. It is also shown in particular examples how certain short operators which one might combine to form long multiplets due to group theoretic considerations may be protected dynamically
Partition Function of the Ising Model via Factor Graph Duality
Molkaraie, Mehdi
2013-01-01
The partition function of a factor graph and the partition function of the dual factor graph are related to each other by the normal factor graph duality theorem. We apply this result to the classical problem of computing the partition function of the Ising model. In the one-dimensional case, we thus obtain an alternative derivation of the (well-known) analytical solution. In the two-dimensional case, we find that Monte Carlo methods are much more efficient on the dual graph than on the original graph, especially at low temperature.
Graph theory and Pfaffian representations of Ising partition function
Gobron, Thierry
2013-01-01
48 pages A well known theorem due to Kasteleyn states that the partition function of an Ising model on an arbitrary planar graph can be represented as the Pfaffian of a skew-symmetric matrix associated to the graph. This results both embodies the free fermionic nature of any planar Ising model and eventually gives an effective way of computing its partition functions in closed form. An extension of this result to non planar models expresses the partition function as a sum of Pfaffians whic...
String partition functions in Rindler space and maximal acceleration
Mertens, Thomas G; Zakharov, Valentin I
2015-01-01
We revisit non-interacting string partition functions in Rindler space by summing over fields in the spectrum. Using recent results of JHEP 1505 (2015) 106, this construction, first done by Emparan, can be put on much firmer ground. For open strings, we demonstrate that surface contributions to the higher spin fields correspond to open strings piercing the Rindler origin, unifying the higher spin surface contributions in string language. We generalize the construction of these partition functions to type II and heterotic superstrings and demonstrate modular invariance for the resulting partition functions. Also, explicit signs of spacetime supersymmetry are visible. All of these exhibit an IR divergence that can be interpreted as a maximal acceleration with $T_{\\text{crit}} = T_{H}/\\pi$ close to the black hole horizon. Ultimately, these partition functions are not physical, and divergences here should not be viewed as a failure of string theory: maximal acceleration is a feature of a faulty treatment of the h...
The M2/M5 BPS Partition Functions from Supergravity
Silva, Pedro J
2009-01-01
In the framework of the AdS/CFT duality, we calculate the supersymmetric partition function of the superconformal field theories living in the world volume of either $N$ $M2$-branes or $N$ $M5$-branes. We used the dual supergravity partition function in a saddle point approximation over supersymmetric Black Holes. Since our BHs are written in asymptotically global $AdS_{d+1}$ co-ordinates, the dual SCFTs are in $R x S^{d}$ for $d=2,5$. The resulting partition function shows phase transitions, constraints on the phase space and allowed us to identify unstable BPS Black hole in the $AdS$ phase. This configurations should corresponds to unstable configurations in the dual theory. We also report an intriguing relation between the most general Witten Index, computed in the above theories, and our BPS partition functions.
Factorization of S^3/Z_n partition function
Imamura, Yosuke; Yokoyama, Daisuke
2013-01-01
We investigate S^3/Z_n partition function of 3d N = 2 supersymmetric field theories. In a gauge theory the partition function is the sum of the contributions of sectors specified by holonomies, and we should carefully choose the relative signs among the contributions. We argue that the factorization to holomorphic blocks is a useful criterion to determine the signs and propose a formula for them. We show that the orbifold partition function of a general non-gauge theory is correctly factorized provided that we take appropriate relative signs. We also present a few examples of gauge theories. We point out that the sign factor for the orbifold partition function is closely related to a similar sign factor in the lens space index and the 3d index.
On the parity of generalized partition functions, III.
Ben Said, Fethi; Nicolas, Jean-Louis; Zekraoui, Ahlem
2010-01-01
International audience Improving on some results of J.-L. Nicolas, the elements of the set ${\\cal A}={\\cal A}(1+z+z^3+z^4+z^5)$, for which the partition function $p({\\cal A},n)$ (i.e. the number of partitions of $n$ with parts in ${\\cal A}$) is even for all $n\\geq 6$ are determined. An asymptotic estimate to the counting function of this set is also given.
Partition function of the trigonometric SOS model with reflecting end
Filali, Ghali
2010-01-01
We compute the partition function of the trigonometric SOS model with one reflecting end and domain wall type boundary conditions. We show that in this case, instead of a sum of determinants obtained by Rosengren for the SOS model on a square lattice without reflection, the partition function can be represented as a single Izergin determinant. This result is crucial for the study of the Bethe vectors of the spin chains with non-diagonal boundary terms.
Line defects and 5d instanton partition functions
Kim, Hee-Cheol
2016-03-01
We consider certain line defect operators in five-dimensional SUSY gauge theories, whose interaction with the self-dual instantons is described by 1d ADHM-like gauged quantum mechanics constructed by Tong and Wong. The partition function in the presence of these operators is known to be a generating function of BPS Wilson loops in skew symmetric tensor representations of the gauge group. We calculate the partition function and explicitly prove that it is a finite polynomial of the defect mass parameter x, which is an essential property of the defect operator and the Wilson loop generating function. The relation between the line defect partition function and the qq-character defined by N . Nekrasov is briefly discussed.
Line defects and 5d instanton partition functions
Kim, Hee-Cheol
2016-01-01
We consider certain line defect operators in five-dimensional SUSY gauge theories, whose interaction with the self-dual instantons is described by 1d ADHM-like gauged quantum mechanics constructed by Tong and Wong. The partition function in the presence of these operators is known to be a generating function of BPS Wilson loops in skew symmetric tensor representations of the gauge group. We calculate the partition function and explicitly prove that it is a finite polynomial of the defect mass parameter $x$, which is an essential property of the defect operator and the Wilson loop generating function. The relation between the line defect partition function and the qq-character defined by N. Nekrasov is briefly discussed.
A brief history of partitions of numbers, partition functions and their modern applications
Debnath, Lokenath
2016-04-01
'Number rules the universe.' The Pythagoras 'If you wish to forsee the future of mathematics our course is to study the history and present conditions of the science.' Henri Poincaré 'The primary source (Urqell) of all mathematics are integers.' Hermann Minkowski This paper is written to commemorate the centennial anniversary of the Mathematical Association of America. It deals with a short history of different kinds of natural numbers including triangular, square, pentagonal, hexagonal and k-gonal numbers, and their simple properties and their geometrical representations. Included are Euclid's and Pythagorean's main contributions to elementary number theory with the main contents of the Euclid Elements of the 13-volume masterpiece of mathematical work. This is followed by Euler's new discovery of the additive number theory based on partitions of numbers. Special attention is given to many examples, Euler's theorems on partitions of numbers with geometrical representations of Ferrers' graphs, Young's diagrams, Lagrange's four-square theorem and the celebrated Waring problem. Included are Euler's generating functions for the partitions of numbers, Euler's pentagonal number theorem, Gauss' triangular and square number theorems and the Jacobi triple product identity. Applications of the theory of partitions of numbers to different statistics such as the Bose- Einstein, Fermi- Dirac, Gentile, and Maxwell- Boltzmann statistics are briefly discussed. Special attention is given to pedagogical information through historical approach to number theory so that students and teachers at the school, college and university levels can become familiar with the basic concepts of partitions of numbers, partition functions and their modern applications, and can pursue advanced study and research in analytical and computational number theory.
Partition function of massless scalar field in Schwarzschild background
Sanyal, Abhik Kumar
2014-01-01
Using thermal value of zeta function instead of zero temperature, the partition function of quantized fields in arbitrary stationary backgrounds was found to be independent of undetermined regularization constant in even-dimension and the long drawn problem associated with the trace anomaly effect had been removed. Here, we explicitly calculate the expression for the coincidence limit so that the technique may be applied in some specific problems. A particular problem dealt with here is to calculate the partition function of massless scalar field in Schwarzschild background.
Canonical and alternate functions of the microRNA biogenesis machinery
Chong, Mark M.W.; Zhang, Guoan; Cheloufi, Sihem; Neubert, Thomas A.; Hannon, Gregory J.; Littman, Dan R.
2010-01-01
The canonical microRNA (miRNA) biogenesis pathway requires two RNaseIII enzymes: Drosha and Dicer. To understand their functions in mammals in vivo, we engineered mice with germline or tissue-specific inactivation of the genes encoding these two proteins. Changes in proteomic and transcriptional profiles that were shared in Dicer- and Drosha-deficient mice confirmed the requirement for both enzymes in canonical miRNA biogenesis. However, deficiency in Drosha or Dicer did not always result in ...
Graphs of partitions and Ramanujan's tau-function
Brent, Barry
2004-01-01
The invariant z_{lambda} attached to a partition lambda sits in the denominator of the Girard-Waring solution to Newton's symmetric function relations. We interpret Ramanujan's tau-function in terms of z_lambda, and interpret z_lambda in terms of the automorphisms of a graph.
Constraints on Fluid Dynamics from Equilibrium Partition Functions
Banerjee, Nabamita; Bhattacharyya, Sayantani; Jain, Sachin; Minwalla, Shiraz; Sharma, Tarun
2012-01-01
We study the thermal partition function of quantum field theories on arbitrary stationary background spacetime, and with arbitrary stationary background gauge fields, in the long wavelength expansion. We demonstrate that the equations of relativistic hydrodynamics are significantly constrained by the requirement of consistency with any partition function. In examples at low orders in the derivative expansion we demonstrate that these constraints coincide precisely with the equalities between hydrodynamical transport coefficients that follow from the local form of the second law of thermodynamics. In particular we recover the results of Son and Surowka on the chiral magnetic and chiral vorticity flows, starting from a local partition function that manifestly reproduces the field theory anomaly, without making any reference to an entropy current. We conjecture that the relations between transport coefficients that follow from the second law of thermodynamics agree to all orders in the derivative expansion with ...
Approximation methods for the partition functions of anharmonic systems
International Nuclear Information System (INIS)
The analytical approximations for the classical, quantum mechanical and reduced partition functions of the diatomic molecule oscillating internally under the influence of the Morse potential have been derived and their convergences have been tested numerically. This successful analytical method is used in the treatment of anharmonic systems. Using Schwinger perturbation method in the framework of second quantization formulism, the reduced partition function of polyatomic systems can be put into an expression which consists separately of contributions from the harmonic terms, Morse potential correction terms and interaction terms due to the off-diagonal potential coefficients. The calculated results of the reduced partition function from the approximation method on the 2-D and 3-D model systems agree well with the numerical exact calculations
Revisiting noninteracting string partition functions in Rindler space
Mertens, Thomas G.; Verschelde, Henri; Zakharov, Valentin I.
2016-05-01
We revisit noninteracting string partition functions in Rindler space by summing over fields in the spectrum. In field theory, the total partition function splits in a natural way into a piece that does not contain surface terms and a piece consisting of solely the so-called edge states. For open strings, we illustrate that surface contributions to the higher-spin fields correspond to open strings piercing the Rindler origin, unifying the higher-spin surface contributions in string language. For closed strings, we demonstrate that the string partition function is not quite the same as the sum over the partition functions of the fields in the spectrum: an infinite overcounting is present for the latter. Next we study the partition functions obtained by excluding the surface terms. Using recent results of He et al. [J. High Energy Phys. 05 (2015) 106], this construction, first done by Emparan [arXiv:hep-th/9412003], can be put on much firmer ground. We generalize to type II and heterotic superstrings and demonstrate modular invariance. All of these exhibit an IR divergence that can be interpreted as a maximal acceleration close to the black hole horizon. Ultimately, since these partition functions are only part of the full story, divergences here should not be viewed as a failure of string theory: maximal acceleration is a feature of a faulty treatment of the higher-spin fields in the string spectrum. We comment on the relevance of this to Solodukhin's recent proposal [Phys. Rev. D 91, 084028 (2015)]. A possible link with the firewall paradox is apparent.
One-loop partition functions of 3D gravity
International Nuclear Information System (INIS)
We consider the one-loop partition function of free quantum field theory in locally Anti-de Sitter space-times. In three dimensions, the one loop determinants for scalar, gauge and graviton excitations are computed explicitly using heat kernel techniques. We obtain precisely the result anticipated by Brown and Henneaux: the partition function includes a sum over 'boundary excitations' of AdS3, which are the Virasoro descendants of empty Anti-de Sitter space. This result also allows us to compute the one-loop corrections to the Euclidean action of the BTZ black hole as well its higher genus generalizations.
International Nuclear Information System (INIS)
Nested Sampling (NS) is a powerful athermal statistical mechanical sampling technique that directly calculates the partition function, and hence gives access to all thermodynamic quantities in absolute terms, including absolute free energies and absolute entropies. NS has been used predominately to compute the canonical (NVT) partition function. Although NS has recently been used to obtain the isothermal-isobaric (NPT) partition function of the hard sphere model, a general approach to the computation of the NPT partition function has yet to be developed. Here, we describe an isobaric NS (IBNS) method which allows for the computation of the NPT partition function of any atomic system. We demonstrate IBNS on two finite Lennard-Jones systems and confirm the results through comparison to parallel tempering Monte Carlo. Temperature-entropy plots are constructed as well as a simple pressure-temperature phase diagram for each system. We further demonstrate IBNS by computing part of the pressure-temperature phase diagram of a Lennard-Jones system under periodic boundary conditions
Wilson, Blake A; Gelb, Lev D; Nielsen, Steven O
2015-10-21
Nested Sampling (NS) is a powerful athermal statistical mechanical sampling technique that directly calculates the partition function, and hence gives access to all thermodynamic quantities in absolute terms, including absolute free energies and absolute entropies. NS has been used predominately to compute the canonical (NVT) partition function. Although NS has recently been used to obtain the isothermal-isobaric (NPT) partition function of the hard sphere model, a general approach to the computation of the NPT partition function has yet to be developed. Here, we describe an isobaric NS (IBNS) method which allows for the computation of the NPT partition function of any atomic system. We demonstrate IBNS on two finite Lennard-Jones systems and confirm the results through comparison to parallel tempering Monte Carlo. Temperature-entropy plots are constructed as well as a simple pressure-temperature phase diagram for each system. We further demonstrate IBNS by computing part of the pressure-temperature phase diagram of a Lennard-Jones system under periodic boundary conditions. PMID:26493898
Energy Technology Data Exchange (ETDEWEB)
Wilson, Blake A.; Nielsen, Steven O. [Department of Chemistry, University of Texas at Dallas, Richardson, Texas 75080 (United States); Gelb, Lev D. [Department of Materials Science and Engineering, University of Texas at Dallas, Richardson, Texas 75080 (United States)
2015-10-21
Nested Sampling (NS) is a powerful athermal statistical mechanical sampling technique that directly calculates the partition function, and hence gives access to all thermodynamic quantities in absolute terms, including absolute free energies and absolute entropies. NS has been used predominately to compute the canonical (NVT) partition function. Although NS has recently been used to obtain the isothermal-isobaric (NPT) partition function of the hard sphere model, a general approach to the computation of the NPT partition function has yet to be developed. Here, we describe an isobaric NS (IBNS) method which allows for the computation of the NPT partition function of any atomic system. We demonstrate IBNS on two finite Lennard-Jones systems and confirm the results through comparison to parallel tempering Monte Carlo. Temperature-entropy plots are constructed as well as a simple pressure-temperature phase diagram for each system. We further demonstrate IBNS by computing part of the pressure-temperature phase diagram of a Lennard-Jones system under periodic boundary conditions.
Grand canonical potential of a magnetized neutron gas
Diener, Jacobus P W
2015-01-01
We compute the effective action for stationary and spatially constant magnetic fields, when coupled anomalously to charge neutral fermions, by integrating out the fermions. From this the grand canonical partition function and potential of the fermions and fields are computed. This also takes care of magnetic field dependent vacuum corrections to the grand canonical potential. Possible applications to neutron stars are indicated.
Identification of plasmid partition function in coryneform bacteria.
Kurusu, Y; Satoh, Y.; Inui, M.; Kohama, K; Kobayashi, M.; Terasawa, M.; Yukawa, H
1991-01-01
We have identified and characterized a partition function that is required for stable maintenance of plasmids in the coryneform bacteria Brevibacterium flavum MJ233 and Corynebacterium glutamicum ATCC 31831. This function is localized to a HindIII-NspV fragment (673 bp) adjacent to the replication region of the plasmid, named pBY503, from Brevibacterium stationis IFO 12144. The function was independent of copy number control and was not associated directly with plasmid replication functions. ...
Popovas, Andrius
2016-01-01
Aims. In this work we rigorously show the shortcomings of various simplifications that are used to calculate the total internal partition function. These shortcomings can lead to errors of up to 40 percent or more in the estimated partition function. These errors carry on to calculations of thermodynamic quantities. Therefore a more complicated approach has to be taken. Methods. Seven possible simplifications of various complexity are described, together with advantages and disadvantages of direct summation of experimental values. These were compared to what we consider the most accurate and most complete treatment (case 8). Dunham coefficients were determined from experimental and theoretical energy levels of a number of electronically excited states of H$_2$ . Both equilibrium and normal hydrogen was taken into consideration. Results. Various shortcomings in existing calculations are demonstrated, and the reasons for them are explained. New partition functions for equilibrium, normal, and ortho and para hyd...
Partitions, rooks, and symmetric functions in noncommuting variables
Can, Mahir Bilen
2010-01-01
Let $\\Pi_n$ denote the set of all set partitions of $\\{1,2,\\ldots,n\\}$. We consider two subsets of $\\Pi_n$, one connected to rook theory and one associated with symmetric functions in noncommuting variables. Let $\\cE_n\\sbe\\Pi_n$ be the subset of all partitions corresponding to an extendable rook (placement) on the upper-triangular board, $\\cT_{n-1}$. Given $\\pi\\in\\Pi_m$ and $\\si\\in\\Pi_n$, define their {\\it slash product\\/} to be $\\pi|\\si=\\pi\\cup(\\si+m)\\in\\Pi_{m+n}$ where $\\si+m$ is the partition obtained by adding $m$ to every element of every block of $\\si$. Call $\\tau$ {\\it atomic\\/} if it can not be written as a nontrivial slash product and let $\\cA_n\\sbe\\Pi_n$ denote the subset of atomic partitions. Atomic partitions were first defined by Bergeron, Hohlweg, Rosas, and Zabrocki during their study of $NCSym$, the symmetric functions in noncommuting variables. We show that, despite their very different definitions, $\\cE_n=\\cA_n$ for all $n\\ge0$. Furthermore, we put an algebra structure on the formal vector s...
Zeta Function Expression of Spin Partition Functions on Thermal AdS3
Directory of Open Access Journals (Sweden)
Floyd L.Williams
2015-07-01
Full Text Available We find a Selberg zeta function expression of certain one-loop spin partition functions on three-dimensional thermal anti-de Sitter space. Of particular interest is the partition function of higher spin fermionic particles. We also set up, in the presence of spin, a Patterson-type formula involving the logarithmic derivative of zeta.
Two loop partition function in (compactified) heterotic string vacua
International Nuclear Information System (INIS)
Two loop partition function for the heterotic string theory, compactified on any background preserving space-time supersymmetry at the string tree level, is explicitly calculated. This includes E8 x E8 or SO(32) heterotic string theory in ten dimensional flat space-time
Quantization of the canonical tensor model and an exact wave function
International Nuclear Information System (INIS)
Tensor models in various forms are being studied as models of quantum gravity. Among them the canonical tensor model has a canonical pair of rank-three tensors as dynamical variables, and is a pure constraint system with first-class constraints. The Poisson algebra of the first-class constraints provides an algebraically consistent way of discretizing the Dirac algebra for general relativity. This paper successfully formulates the Wheeler-DeWitt quantization of the canonical tensor model. Formally one can obtain wave functions of the ''universe'' by solving the partial differential equations representing the constraints. For the simplest non-trivial case, the unique wave function is exactly and globally obtained. Although this case is far from being realistic, the wave function is physically interesting; locality is favored, and there exists a locus of configurations with features of the beginning of the universe
Canonical self-affine tilings by iterated function systems
Pearse, Erin P. J.
2006-01-01
An iterated function system $\\Phi$ consisting of contractive similarity mappings has a unique attractor $F \\subseteq \\mathbb{R}^d$ which is invariant under the action of the system, as was shown by Hutchinson [Hut]. This paper shows how the action of the function system naturally produces a tiling $\\mathcal{T}$ of the convex hull of the attractor. More precisely, it tiles the complement of the attractor within its convex hull. These tiles form a collection of sets whose geometry is typically ...
$q$-Virasoro modular double and 3d partition functions
Nedelin, Anton; Zabzine, Maxim
2016-01-01
We study partition functions of 3d $\\mathcal{N}=2$ U(N) gauge theories on compact manifolds which are $S^1$ fibrations over $S^2$. We show that the partition functions are free field correlators of vertex operators and screening charges of the $q$-Virasoro modular double, which we define. The inclusion of supersymmetric Wilson loops in arbitrary representations allows us to show that the generating functions of Wilson loop vacuum expectation values satisfy two SL(2,$\\mathbb{Z}$)-related commuting sets of $q$-Virasoro constraints. We generalize our construction to 3d $\\mathcal{N}=2$ unitary quiver gauge theories and as an example we give the free boson realization of the ABJ(M) model.
Identification of plasmid partition function in coryneform bacteria
Energy Technology Data Exchange (ETDEWEB)
Kurusu, Yasurou; Satoh, Yukie; Inui, Masayuki; Kohama, Keiko; Kobayashi, Miki; Terasawa, Masato; Yukawa, Hideaki (Mitsubishi Petrochemical Co., Ltd., Ibaraki (Japan))
1991-03-01
The authors have identified and characterized a partition function that is required for stable maintenance of plasmids in the coryneform bacteria Brevibacterium flavum MJ233 and Corynebacterium glutamicum ATCC 31831. This function is localized to a HindIII-NspV fragment (673 bp) adjacent to the replication region of the plasmid, named pBY503, from Brevibacterium stationis IFO 12144. The function was independent of copy number control and was not associated directly with plasmid replication functions. This fragment was able to stabilize the unstable plasmids in cis but not in trans.
\\beta-deformed matrix model and Nekrasov partition function
Nishinaka, Takahiro
2011-01-01
We study Penner type matrix models in relation with the Nekrasov partition function of four dimensional \\mathcal{N}=2, SU(2) supersymmetric gauge theories with N_F=2,3 and 4. By evaluating the resolvent using the loop equation for general \\beta, we explicitly construct the first half-genus correction to the free energy and demonstrate the result coincides with the corresponding Nekrasov partition function with general \\Omega-background, including higher instanton contributions after modifying the relation of the Coulomb branch parameter with the filling fraction. Our approach complements the proof using the Selberg integrals directly which is useful to find the contribution in the series of instanton numbers for a given deformation parameter.
β-deformed matrix model and Nekrasov partition function
Nishinaka, Takahiro; Rim, Chaiho
2012-02-01
We study Penner type matrix models in relation with the Nekrasov partition function of four dimensional mathcal{N} = {2} , SU(2) supersymmetric gauge theories with N F = 2 , 3 and 4. By evaluating the resolvent using the loop equation for general β, we explicitly construct the first half-genus correction to the free energy and demonstrate the result coincides with the corresponding Nekrasov partition function with general Ω-background, including higher instanton contributions after modifying the relation of the Coulomb branch parameter with the filling fraction. Our approach complements the proof using the Selberg integrals directly which is useful to find the contribution in the series of instanton numbers for a given deformation parameter.
Unified approach to partition functions of RNA secondary structures.
Bundschuh, Ralf
2014-11-01
RNA secondary structure formation is a field of considerable biological interest as well as a model system for understanding generic properties of heteropolymer folding. This system is particularly attractive because the partition function and thus all thermodynamic properties of RNA secondary structure ensembles can be calculated numerically in polynomial time for arbitrary sequences and homopolymer models admit analytical solutions. Such solutions for many different aspects of the combinatorics of RNA secondary structure formation share the property that the final solution depends on differences of statistical weights rather than on the weights alone. Here, we present a unified approach to a large class of problems in the field of RNA secondary structure formation. We prove a generic theorem for the calculation of RNA folding partition functions. Then, we show that this approach can be applied to the study of the molten-native transition, denaturation of RNA molecules, as well as to studies of the glass phase of random RNA sequences. PMID:24177391
High-Temperature Expansion of Supersymmetric Partition Functions
Ardehali, Arash Arabi; Szepietowski, Phillip
2015-01-01
Di Pietro and Komargodski have recently demonstrated a four-dimensional counterpart of Cardy's formula, which gives the leading high-temperature ($\\beta \\rightarrow 0$) behavior of supersymmetric partition functions $Z^{SUSY}(\\beta)$. Focusing on superconformal theories, we elaborate on the subleading contributions to their formula when applied to free chiral and U(1) vector multiplets. In particular, we see that the high-temperature expansion of $\\ln Z^{SUSY}(\\beta)$ terminates at order $\\beta^0$. We also demonstrate how their formula must be modified when applied to SU($N$) toric quiver gauge theories in the planar ($N \\rightarrow \\infty$) limit. Our method for regularizing the one-loop determinants of chiral and vector multiplets helps to clarify the relation between the 4d $\\mathcal{N} = 1$ superconformal index and its corresponding supersymmetric partition function obtained by path-integration.
Computing black hole partition functions from quasinormal modes
Arnold, Peter; Vaman, Diana
2016-01-01
We propose a method of computing one-loop determinants in black hole spacetimes (with emphasis on asymptotically anti-de Sitter black holes) that may be used for numerics when completely-analytic results are unattainable. The method utilizes the expression for one-loop determinants in terms of quasinormal frequencies determined by Denef, Hartnoll and Sachdev in [1]. A necessary ingredient is a refined regularization scheme to regulate the contributions of individual fixed-momentum sectors to the partition function. To this end, we formulate an effective two-dimensional problem in which a natural refinement of standard heat kernel techniques can be used to account for contributions to the partition function at fixed momentum. We test our method in a concrete case by reproducing the scalar one-loop determinant in the BTZ black hole background. We then discuss the application of such techniques to more complicated spacetimes.
The Partition Function of Multicomponent Log-Gases
Sinclair, Christopher D
2012-01-01
We give an expression for the partition function of a one-dimensional log-gas comprised of particles of (possibly) different integer charge at inverse temperature {\\beta} = 1 (restricted to the line in the presence of a neutralizing field) in terms of the Berezin integral of an associated non- homogeneous alternating tensor. This is the analog of the de Bruijn integral identities [3] (for {\\beta} = 1 and {\\beta} = 4) ensembles extended to multicomponent ensembles.
Factorized domain wall partition functions in trigonometric vertex models
Foda, O; Zuparic, M
2007-01-01
We obtain factorized domain wall partition functions for two sets of trigonometric vertex models: 1. The N-state Deguchi-Akutsu models, for N = {2, 3, 4} (and conjecture the result for all N >= 5), and 2. The sl(r+1|s+1) Perk-Schultz models, for {r, s = \\N}, where (given the symmetries of these models) the result is independent of {r, s}.
Factorized domain wall partition functions in trigonometric vertex models
Foda, O.; Wheeler, M.; Zuparic, M.
2007-10-01
We obtain factorized domain wall partition functions for two sets of trigonometric vertex models: (1) the N-state Deguchi Akutsu models, for N \\in \\{2, 3, 4\\} (and conjecture the result for all N>=5), and (2) the sl(r+1|s+1) Perk Schultz models, for \\{r, s \\in \\mathbb {N}\\} , where (given the symmetries of these models) the result is independent of {r,s}.
Anyonic partition functions and windings of planar Brownian motion
International Nuclear Information System (INIS)
The computation of the N-cycle Brownian paths contribution FN(α) to the N-anyon partition function is addressed. A detailed numerical analysis based on a random walk on a lattice indicates that FN0(α)=product k=1N-1[1-(N/k)α]. In the paramount three-anyon case, one can show that F3(α) is built by linear states belonging to the bosonic, fermionic, and mixed representations of S3
Conformal transformations and the SLE partition function martingale
Bauer, Michel; Bernard, Denis
2003-01-01
We present an implementation in conformal field theory (CFT) of local finite conformal transformations fixing a point. We give explicit constructions when the fixed point is either the origin or the point at infinity. Both cases involve the exponentiation of a Borel subalgebra of the Virasoro algebra. We use this to build coherent state representations and to derive a close analog of Wick's theorem for the Virasoro algebra. This allows to compute the conformal partition function in non trivia...
High-temperature asymptotics of supersymmetric partition functions
Ardehali, Arash Arabi
2015-01-01
We study the partition function of 4d supersymmetric gauge theories with an R-symmetry on Euclidean $S^3\\times S_\\beta^1$, with $S^3$ the unit-radius squashed three-sphere, and $\\beta$ the circumference of the circle. For superconformal theories, this partition function coincides (up to a Casimir energy factor) with the 4d superconformal index. The partition function can be computed exactly using supersymmetric localization of the gauge theory path-integral. It takes the form of an elliptic hypergeometric integral, which may be viewed as a matrix-integral over the moduli space of the holonomies of the gauge fields around $S_\\beta^1$. At high temperatures ($\\beta\\to 0$, corresponding to the hyperbolic limit of the elliptic hypergeometric integral) we obtain from the matrix-integral a quantum effective potential for the holonomies. The effective potential is proportional to the temperature. Therefore the high-temperature limit further localizes the matrix-integral to the locus of the minima of the potential. If...
Some bounds on quantum partition functions by path-integral methods
International Nuclear Information System (INIS)
Equilibrium statistical mechanics requires the competition of the partition function. The density matrix and hence the quantum partition function may be expressed as an integral with an integral which can be given explicitly, namely as a (Wiener-) path integral. Techniques especially designed for path integrals provide inequalities for density matrices, partition functions and spectral densities. Some of these inequalities related to density matrices and partition functions are reviewed in this paper. 39 refs
Generalised partition functions: inferences on phase space distributions
Treumann, Rudolf A.; Baumjohann, Wolfgang
2016-06-01
It is demonstrated that the statistical mechanical partition function can be used to construct various different forms of phase space distributions. This indicates that its structure is not restricted to the Gibbs-Boltzmann factor prescription which is based on counting statistics. With the widely used replacement of the Boltzmann factor by a generalised Lorentzian (also known as the q-deformed exponential function, where κ = 1/|q - 1|, with κ, q ∈ R) both the kappa-Bose and kappa-Fermi partition functions are obtained in quite a straightforward way, from which the conventional Bose and Fermi distributions follow for κ → ∞. For κ ≠ ∞ these are subject to the restrictions that they can be used only at temperatures far from zero. They thus, as shown earlier, have little value for quantum physics. This is reasonable, because physical κ systems imply strong correlations which are absent at zero temperature where apart from stochastics all dynamical interactions are frozen. In the classical large temperature limit one obtains physically reasonable κ distributions which depend on energy respectively momentum as well as on chemical potential. Looking for other functional dependencies, we examine Bessel functions whether they can be used for obtaining valid distributions. Again and for the same reason, no Fermi and Bose distributions exist in the low temperature limit. However, a classical Bessel-Boltzmann distribution can be constructed which is a Bessel-modified Lorentzian distribution. Whether it makes any physical sense remains an open question. This is not investigated here. The choice of Bessel functions is motivated solely by their convergence properties and not by reference to any physical demands. This result suggests that the Gibbs-Boltzmann partition function is fundamental not only to Gibbs-Boltzmann but also to a large class of generalised Lorentzian distributions as well as to the corresponding nonextensive statistical mechanics.
Getting full control of canonical correlation analysis with the AutoBiplot.CCA function
Alves, M. Rui
2016-06-01
Function AutoBiplot.CCA was built in R language. Given two multivariate data sets, this function carries out a conventional canonical correlation analysis, followed by the automatic production of predictive biplots based on the accuracy of readings as assessed by a mean standard predictive error and a user defined tolerance value. As the user's intervention is mainly restricted to the choice of the magnitude of the t.axis value, common misinterpretations, overestimations and adjustments between outputs and personal beliefs are avoided.
Energy Technology Data Exchange (ETDEWEB)
Catoni, Francesco; Zampetti, Paolo [ENEA, Centro Ricerche Casaccia, Rome (Italy). Dipt. Energia; Cannata, Roberto [ENEA, Centro Ricerche Casaccia, Rome (Italy). Funzione Centrale INFO; Nichelatti, Enrico [ENEA, Centro Ricerche Casaccia, Rome (Italy). Dipt. Innovazione
1997-10-01
Systems of two-dimensional hypercomplex numbers are usually studied in their canonical form, i.e. according to the multiplicative rule for the ``imaginary``versor i{sup 2} = {+-} 1, 0. In this report those systems for which i{sup 2} = {alpha} + {beta}i are studied and expressions are derived for functions given by series expansion as well as for some elementary functions. The results obtained for systems which can be decomposed are then extended to all systems.
Random trees between two walls: exact partition function
International Nuclear Information System (INIS)
We derive the exact partition function for a discrete model of random trees embedded in a one-dimensional space. These trees have vertices labelled by integers representing their position in the target space, with the solid-on-solid constraint that adjacent vertices have labels differing by ±1. A non-trivial partition function is obtained whenever the target space is bounded by walls. We concentrate on the two cases where the target space is (i) the half-line bounded by a wall at the origin or (ii) a segment bounded by two walls at a finite distance. The general solution has a soliton-like structure involving elliptic functions. We derive the corresponding continuum scaling limit which takes the remarkable form of the Weierstrass p function with constrained periods. These results are used to analyse the probability for an evolving population spreading in one dimension to attain the boundary of a given domain with the geometry of the target (i) or (ii). They also translate, via suitable bijections, into generating functions for bounded planar graphs
1 Taiwo O. A
2013-01-01
The problem of solving special nth-order linear integro-differential equations has special importance in engineering and sciences that constitutes a good model for many systems in various fields. In this paper, we construct canonical polynomial from the differential parts of special nth-order integro-differential equations and use it as our basis function for the numerical solutions of special nth-order integro-differential equations. The results obtained by this method are compared with thos...
Semiclassical partition function for the double-well potential
Kroff, D; de Carvalho, C A A; Fraga, E S; Jorás, S E
2013-01-01
We compute the partition function and specific heat for a quantum mechanical particle under the influence of a quartic double-well potential non-perturbatively, using the semiclassical method. Near the region of bounded motion in the inverted potential, the usual quadratic approximation fails due to the existence of multiple classical solutions and caustics. Using the tools of catastrophe theory, we identify the relevant classical solutions, showing that at most two have to be considered. This corresponds to the first step towards the study of spontaneous symmetry breaking and thermal phase transitions in the non-perturbative framework of the boundary effective theory.
Non-perturbative Nekrasov partition function from string theory
International Nuclear Information System (INIS)
We calculate gauge instanton corrections to a class of higher derivative string effective couplings introduced in [1]. We work in Type I string theory compactified on K3×T2 and realise gauge instantons in terms of D5-branes wrapping the internal space. In the field theory limit we reproduce the deformed ADHM action on a general Ω-background from which one can compute the non-perturbative gauge theory partition function using localisation. This is a non-perturbative extension of [1] and provides further evidence for our proposal of a string theory realisation of the Ω-background
Holographic partition functions and phases for higher genus Riemann surfaces
Maxfield, Henry; Ross, Simon F.; Way, Benson
2016-06-01
We describe a numerical method to compute the action of Euclidean saddle points for the partition function of a two-dimensional holographic CFT on a Riemann surface of arbitrary genus, with constant curvature metric. We explicitly evaluate the action for the saddles for genus two and map out the phase structure of dominant bulk saddles in a two-dimensional subspace of the moduli space. We discuss spontaneous breaking of discrete symmetries, and show that the handlebody bulk saddles always dominate over certain non-handlebody solutions.
Ratios of partition functions for the log-gamma polymer
Georgiou, Nicos; Rassoul-Agha, Firas; Seppalainen, Timo; Yilmaz, Atilla
2015-01-01
The Annals of Probability 2015, Vol. 43, No. 5, 2282–2331 DOI: 10.1214/14-AOP933 © Institute of Mathematical Statistics, 2015 RATIOS OF PARTITION FUNCTIONS FOR THE LOG-GAMMA POLYMER BY NICOS GEORGIOU1, FIRAS RASSOUL-AGHA1, TIMO SEPPÄLÄINEN2 AND ATILLA YILMAZ3 University of Sussex, University of Utah, University of Wisconsin–Madison and Bo˘gaziçi University We introduce a random walk in random environment associated to an underlying directed polymer model in 1 ...
Holographic partition functions and phases for higher genus Riemann surfaces
Maxfield, Henry; Way, Benson
2016-01-01
We describe a numerical method to compute the action of Euclidean saddlepoints for the partition function of a two-dimensional holographic CFT on a Riemann surface of arbitrary genus, with constant curvature metric. We explicitly evaluate the action for the saddles for genus two and map out the phase structure of dominant bulk saddles in a two-dimensional subspace of the moduli space. We discuss spontaneous breaking of discrete symmetries, and show that the handlebody bulk saddles always dominate over certain non-handlebody solutions.
Anyonic Partition Functions and Windings of Planar Brownian Motion
Desbois, Jean; Heinemann, Christine; Ouvry, Stéphane
1994-01-01
The computation of the $N$-cycle brownian paths contribution $F_N(\\alpha)$ to the $N$-anyon partition function is adressed. A detailed numerical analysis based on random walk on a lattice indicates that $F_N^{(0)}(\\alpha)= \\prod_{k=1}^{N-1}(1-{N\\over k}\\alpha)$. In the paramount $3$-anyon case, one can show that $F_3(\\alpha)$ is built by linear states belonging to the bosonic, fermionic, and mixed representations of $S_3$.
Canonical and alternate functions of the microRNA biogenesis machinery.
Chong, Mark M W; Zhang, Guoan; Cheloufi, Sihem; Neubert, Thomas A; Hannon, Gregory J; Littman, Dan R
2010-09-01
The canonical microRNA (miRNA) biogenesis pathway requires two RNaseIII enzymes: Drosha and Dicer. To understand their functions in mammals in vivo, we engineered mice with germline or tissue-specific inactivation of the genes encoding these two proteins. Changes in proteomic and transcriptional profiles that were shared in Dicer- and Drosha-deficient mice confirmed the requirement for both enzymes in canonical miRNA biogenesis. However, deficiency in Drosha or Dicer did not always result in identical phenotypes, suggesting additional functions. We found that, in early-stage thymocytes, Drosha recognizes and directly cleaves many protein-coding messenger RNAs (mRNAs) with secondary stem-loop structures. In addition, we identified a subset of miRNAs generated by a Dicer-dependent but Drosha-independent mechanism. These were distinct from previously described mirtrons. Thus, in mammalian cells, Dicer is required for the biogenesis of multiple classes of miRNAs. Together, these findings extend the range of function of RNaseIII enzymes beyond canonical miRNA biogenesis, and help explain the nonoverlapping phenotypes caused by Drosha and Dicer deficiency. PMID:20713509
Minimal models on Riemann surfaces: The partition functions
Energy Technology Data Exchange (ETDEWEB)
Foda, O. (Katholieke Univ. Nijmegen (Netherlands). Inst. voor Theoretische Fysica)
1990-06-04
The Coulomb gas representation of the A{sub n} series of c=1-6/(m(m+1)), m{ge}3, minimal models is extended to compact Riemann surfaces of genus g>1. An integral representation of the partition functions, for any m and g is obtained as the difference of two gaussian correlation functions of a background charge, (background charge on sphere) x (1-g), and screening charges integrated over the surface. The coupling constant x (compacitification radius){sup 2} of the gaussian expressions are, as on the torus, m(m+1), and m/(m+1). The partition functions obtained are modular invariant, have the correct conformal anomaly and - restricting the propagation of states to a single handle - one can verify explicitly the decoupling of the null states. On the other hand, they are given in terms of coupled surface integrals, and it remains to show how they degenerate consistently to those on lower-genus surfaces. In this work, this is clear only at the lattice level, where no screening charges appear. (orig.).
Minimal models on Riemann surfaces: The partition functions
International Nuclear Information System (INIS)
The Coulomb gas representation of the An series of c=1-6/[m(m+1)], m≥3, minimal models is extended to compact Riemann surfaces of genus g>1. An integral representation of the partition functions, for any m and g is obtained as the difference of two gaussian correlation functions of a background charge, (background charge on sphere) x (1-g), and screening charges integrated over the surface. The coupling constant x (compacitification radius)2 of the gaussian expressions are, as on the torus, m(m+1), and m/(m+1). The partition functions obtained are modular invariant, have the correct conformal anomaly and - restricting the propagation of states to a single handle - one can verify explicitly the decoupling of the null states. On the other hand, they are given in terms of coupled surface integrals, and it remains to show how they degenerate consistently to those on lower-genus surfaces. In this work, this is clear only at the lattice level, where no screening charges appear. (orig.)
Colour-independent partition functions in coloured vertex models
Energy Technology Data Exchange (ETDEWEB)
Foda, O., E-mail: omar.foda@unimelb.edu.au [Dept. of Mathematics and Statistics, University of Melbourne, Parkville, VIC 3010 (Australia); Wheeler, M., E-mail: mwheeler@lpthe.jussieu.fr [Laboratoire de Physique Théorique et Hautes Energies, CNRS UMR 7589 (France); Université Pierre et Marie Curie – Paris 6, 4 place Jussieu, 75252 Paris cedex 05 (France)
2013-06-11
We study lattice configurations related to S{sub n}, the scalar product of an off-shell state and an on-shell state in rational A{sub n} integrable vertex models, n∈{1,2}. The lattice lines are colourless and oriented. The state variables are n conserved colours that flow along the line orientations, but do not necessarily cover every bond in the lattice. Choosing boundary conditions such that the positions where the colours flow into the lattice are fixed, and where they flow out are summed over, we show that the partition functions of these configurations, with these boundary conditions, are n-independent. Our results extend to trigonometric A{sub n} models, and to all n. This n-independence explains, in vertex-model terms, results from recent studies of S{sub 2} (Caetano and Vieira, 2012, [1], Wheeler, (arXiv:1204.2089), [2]). Namely, 1.S{sub 2}, which depends on two sets of Bethe roots, {b_1} and {b_2}, and cannot (as far as we know) be expressed in single determinant form, degenerates in the limit {b_1}→∞, and/or {b_2}→∞, into a product of determinants, 2. Each of the latter determinants is an A{sub 1} vertex-model partition function.
Colour-independent partition functions in coloured vertex models
International Nuclear Information System (INIS)
We study lattice configurations related to Sn, the scalar product of an off-shell state and an on-shell state in rational An integrable vertex models, n∈{1,2}. The lattice lines are colourless and oriented. The state variables are n conserved colours that flow along the line orientations, but do not necessarily cover every bond in the lattice. Choosing boundary conditions such that the positions where the colours flow into the lattice are fixed, and where they flow out are summed over, we show that the partition functions of these configurations, with these boundary conditions, are n-independent. Our results extend to trigonometric An models, and to all n. This n-independence explains, in vertex-model terms, results from recent studies of S2 (Caetano and Vieira, 2012, [1], Wheeler, (arXiv:1204.2089), [2]). Namely, 1.S2, which depends on two sets of Bethe roots, {b1} and {b2}, and cannot (as far as we know) be expressed in single determinant form, degenerates in the limit {b1}→∞, and/or {b2}→∞, into a product of determinants, 2. Each of the latter determinants is an A1 vertex-model partition function
On entire functions restricted to intervals, partition of unities, and dual Gabor frames
DEFF Research Database (Denmark)
Christensen, Ole; Kim, Hong Oh; Kim, Rae Young
2014-01-01
Partition of unities appears in many places in analysis. Typically it is generated by compactly supported functions with a certain regularity. In this paper we consider partition of unities obtained as integer-translates of entire functions restricted to finite intervals. We characterize the entire...... functions that lead to a partition of unity in this way, and we provide characterizations of the “cut-off” entire functions, considered as functions of a real variable, to have desired regularity. In particular we obtain partition of unities generated by functions with small support and desired regularity...
Modular invariant partition function of critical dense polymers
International Nuclear Information System (INIS)
A lattice model of critical dense polymers is solved exactly for arbitrary system size on the torus. More generally, an infinite family of lattice loop models is studied on the torus and related to the corresponding Fortuin–Kasteleyn random cluster models. Starting with a cylinder, the commuting periodic single-row transfer matrices are built from the periodic Temperley–Lieb algebra extended by the shift operators Ω±1. In this enlarged algebra, the non-contractible loop fugacity is α and the contractible loop fugacity is β. The torus is formed by gluing the top and bottom of the cylinder. This gives rise to a variety of non-contractible loops winding around the torus. Because of their nonlocal nature, the standard matrix trace does not produce the proper geometric torus. Instead, we introduce a modified matrix trace for this purpose. This is achieved by using a representation of the enlarged periodic Temperley–Lieb algebra with a parameter v that keeps track of the winding of defects on the cylinder. The transfer matrix representatives and their eigenvalues thus depend on v. The modified trace is constructed as a linear functional on planar connectivity diagrams in terms of matrix traces Trd (with a fixed number of defects d) and Chebyshev polynomials of the first kind. For critical dense polymers, where β=0, the transfer matrix eigenvalues are obtained by solving a functional equation in the form of an inversion identity. The solution depends on d and is subject to selection rules which we prove. Simplifications occur if all non-contractible loop fugacities are set to α=2 in which case the traces are evaluated at v=1. In the continuum scaling limit, the corresponding conformal torus partition function obtained from finite-size corrections agrees with the known modular invariant partition function of symplectic fermions
Hemisphere Partition Function and Analytic Continuation to the Conifold Point
Knapp, Johanna; Scheidegger, Emanuel
2016-01-01
We show that the hemisphere partition function for certain U(1) gauged linear sigma models (GLSMs) with D-branes is related to a particular set of Mellin-Barnes integrals which can be used for analytic continuation to the singular point in the K\\"ahler moduli space of an $h^{1,1}=1$ Calabi-Yau (CY) projective hypersurface. We directly compute the analytic continuation of the full quantum corrected central charge of a basis of geometric D-branes from the large volume to the singular point. In the mirror language this amounts to compute the analytic continuation of a basis of periods on the mirror CY to the conifold point. However, all calculations are done in the GLSM and we do not have to refer to the mirror CY. We apply our methods explicitly to the cubic, quartic and quintic CY hypersurfaces.
Twists of Pl\\"ucker coordinates as dimer partition functions
Scott, Jeanne
2013-01-01
The homogeneous coordinate ring of the Grassmannian Gr(k,n) has a cluster structure defined in terms of planar diagrams known as Postnikov diagrams. The cluster corresponding to such a diagram consists entirely of Pl\\"ucker coordinates. We introduce a twist map on Gr(k,n) related to the BZ-twist, and give an explicit Laurent expansion for the twist of an arbitrary Pl\\"ucker coordinate, in terms of the cluster variables associated with a fixed Postnikov diagram. The expansion arises as a (scaled) dimer partition function of a weighted version of the bipartite graph dual to the Postnikov diagram, modified by a boundary condition determined by the Pl\\"ucker coordinate.
Directory of Open Access Journals (Sweden)
1 Taiwo O. A
2013-01-01
Full Text Available The problem of solving special nth-order linear integro-differential equations has special importance in engineering and sciences that constitutes a good model for many systems in various fields. In this paper, we construct canonical polynomial from the differential parts of special nth-order integro-differential equations and use it as our basis function for the numerical solutions of special nth-order integro-differential equations. The results obtained by this method are compared with those obtained by Adomian Decomposition method. It is also observed that the new method is an effective method with high accuracy. Some examples are given to illustrate the method.
Partition Function of 1-, 2-, and 3-D Monatomic Ideal Gas (a Simple and Comprehensive Review)
Khotimah, Siti Nurul
2011-01-01
This article discusses partition function of monatomic ideal gas which is given in Statistical Physisc at Physics Department, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Indonesia. Students in general are not familiar with partition function. This unfamiliarness was detected at a problem of partition function which was re-given in an examination in other dimensions that had been previously given in the lecture. Based on this observation, the need of a simple but comprehensive article about partition function in one-, two-, and three-dimensions is a must. For simplicity, a monatomic ideal gas is chosen.
Natural Microbial Assemblages Reflect Distinct Organismal and Functional Partitioning
Wilmes, P.; Andersson, A.; Kalnejais, L. H.; Verberkmoes, N. C.; Lefsrud, M. G.; Wexler, M.; Singer, S. W.; Shah, M.; Bond, P. L.; Thelen, M. P.; Hettich, R. L.; Banfield, J. F.
2007-12-01
The ability to link microbial community structure to function has long been a primary focus of environmental microbiology. With the advent of community genomic and proteomic techniques, along with advances in microscopic imaging techniques, it is now possible to gain insights into the organismal and functional makeup of microbial communities. Biofilms growing within highly acidic solutions inside the Richmond Mine (Iron Mountain, Redding, California) exhibit distinct macro- and microscopic morphologies. They are composed of microorganisms belonging to the three domains of life, including archaea, bacteria and eukarya. The proportion of each organismal type depends on sampling location and developmental stage. For example, mature biofilms floating on top of acid mine drainage (AMD) pools exhibit layers consisting of a densely packed bottom layer of the chemoautolithotroph Leptospirillum group II, a less dense top layer composed mainly of archaea, and fungal filaments spanning across the entire biofilm. The expression of cytochrome 579 (the most highly abundant protein in the biofilm, believed to be central to iron oxidation and encoded by Leptospirillum group II) is localized at the interface of the biofilm with the AMD solution, highlighting that biofilm architecture is reflected at the functional gene expression level. Distinct functional partitioning is also apparent in a biological wastewater treatment system that selects for distinct polyphosphate accumulating organisms. Community genomic data from " Candidatus Accumulibacter phosphatis" dominated activated sludge has enabled high mass-accuracy shotgun proteomics for identification of key metabolic pathways. Comprehensive genome-wide alignment of orthologous proteins suggests distinct partitioning of protein variants involved in both core-metabolism and specific metabolic pathways among the dominant population and closely related species. In addition, strain- resolved proteogenomic analysis of the AMD biofilms
Elliptic solid-on-solid model's partition function as a single determinant
Galleas, W
2016-01-01
In this work we express the partition function of the integrable elliptic solid-on-solid model with domain-wall boundary conditions as a single determinant. This representation appears naturally as the solution of a system of functional equations governing the model's partition function.
Smoothed analysis of partitioning algorithms for Euclidean functionals
Bläser, Markus; Manthey, Bodo; Rao, B.V. Raghavendra; Dehne, F.; Iacono, J.; Sack, J.-R.
2011-01-01
Euclidean optimization problems such as TSP and minimum-length matching admit fast partitioning algorithms that compute near-optimal solutions on typical instances. We develop a general framework for the application of smoothed analysis to partitioning algorithms for Euclidean optimization problems.
Smoothed analysis of partitioning algorithms for Euclidean functionals
Bläser, Markus; Manthey, Bodo; Rao, B.V. Raghavendra
2013-01-01
Euclidean optimization problems such as TSP and minimum-length matching admit fast partitioning algorithms that compute near-optimal solutions on typical instances. In order to explain this performance, we develop a general framework for the application of smoothed analysis to partitioning algorithm
Large N techniques for Nekrasov partition functions and AGT conjecture
Bourgine, Jean-Emile
2013-01-01
The AGT conjecture relates \\mathcal{N}=2 4d SUSY gauge theories to 2d CFTs. Matrix model techniques can be used to investigate both sides of this relation. The large N limit refers here to the size of Young tableaux in the expression of the gauge theory partition function. It corresponds to vanishing of Omega-background equivariant deformation parameters, and should not be confused with the t'Hooft expansion at large number of colors. In the first part of the paper, a saddle point approach is employed to study the Nekrasov-Shatshvili limit of the gauge theory, leading to define beta-deformed, or quantized, Seiberg-Witten curve and differential form. In a second part, this formalism is compared to the large N limit of the Dijkgraaf-Vafa beta-ensemble. A transformation law relating the wave functions appearing at both sides of the conjecture is proposed. It implies a transformation of the Seiberg-Witten 1-form in agreement with the definition proposed earlier. As a side result, a remarkable property of the \\mat...
Partition function and base pairing probabilities of RNA heterodimers
Directory of Open Access Journals (Sweden)
Stadler Peter F
2006-03-01
Full Text Available Abstract Background RNA has been recognized as a key player in cellular regulation in recent years. In many cases, non-coding RNAs exert their function by binding to other nucleic acids, as in the case of microRNAs and snoRNAs. The specificity of these interactions derives from the stability of inter-molecular base pairing. The accurate computational treatment of RNA-RNA binding therefore lies at the heart of target prediction algorithms. Methods The standard dynamic programming algorithms for computing secondary structures of linear single-stranded RNA molecules are extended to the co-folding of two interacting RNAs. Results We present a program, RNAcofold, that computes the hybridization energy and base pairing pattern of a pair of interacting RNA molecules. In contrast to earlier approaches, complex internal structures in both RNAs are fully taken into account. RNAcofold supports the calculation of the minimum energy structure and of a complete set of suboptimal structures in an energy band above the ground state. Furthermore, it provides an extension of McCaskill's partition function algorithm to compute base pairing probabilities, realistic interaction energies, and equilibrium concentrations of duplex structures. Availability RNAcofold is distributed as part of the Vienna RNA Package, http://www.tbi.univie.ac.at/RNA/. Contact Stephan H. Bernhart – berni@tbi.univie.ac.at
Polymer quantization and the saddle point approximation of partition functions
Técotl, Hugo A Morales; Rastgoo, Saeed
2015-01-01
The saddle point approximation of the path integral partition functions is an important way of deriving the thermodynamical properties of black holes. However, there are certain black hole models and some mathematically analog mechanical models for which this method can not be applied directly. This is due to the fact that their action evaluated on a classical solution is not finite and its first variation does not vanish for all consistent boundary conditions. These problems can be dealt with by adding a counter-term to the classical action, which is a solution of the corresponding Hamilton-Jacobi equation. In this work we study the effects of polymer quantization on a mechanical model presenting the aforementioned difficulties and contrast it with the above counter-term method. This type of quantization for mechanical models is motivated by the loop quantization of gravity which is known to play a role in the thermodynamics of black holes systems. The model we consider is a non relativistic particle in an i...
Colour-independent partition functions in coloured vertex models
Foda, O
2013-01-01
We study lattice configurations related to S_n, the scalar product of an off-shell state and an on-shell state in rational A_n integrable vertex models, n = {1, 2}. The lattice lines are colourless and oriented. The state variables are n conserved colours that flow along the line orientations, but do not necessarily cover every bond in the lattice. Choosing boundary conditions such that the positions where the colours flow into the lattice are fixed, and where they flow out are summed over, we show that the partition functions of these configurations, with these boundary conditions, are n-independent. Our results extend to trigonometric A_n models, and to all n. This n-independence explains, in vertex-model terms, results from recent studies of S_2 [1, 2]. Namely, 1. S_2 which depends on two sets of Bethe roots, b_1 and b_2, and cannot (as far as we know) be expressed in single determinant form, degenerates in the limit b_1 -> infinity, and/or b_2 -> infinity, into a product of determinants, 2. Each of the la...
International Nuclear Information System (INIS)
Partition functions for a canonical and microcanonical ensemble are developed which are then used to describe various properties of excited hadronic systems. Relating multinomial coefficients to a generating function of these partition functions, it is shown that the average value of various moments of cluster sizes are of a quite simple form in terms of canonical partition functions. Specific applications of the results are to partitioning problems as in the partitioning of nucleons into clusters arising from a nuclear collision and to branching processes as in Furry branching. The underlying dynamical evolution of a system is studied by parametrizing the multinomial variables of the theory. A Fokker-Planck equation can be obtained from these evolutionary equations. By relating the parameters and variables of the theory to thermodynamic variables, the thermal properties of excited hadronic systems are studied
Polymer quantization and the saddle point approximation of partition functions
Morales-Técotl, Hugo A.; Orozco-Borunda, Daniel H.; Rastgoo, Saeed
2015-11-01
The saddle point approximation of the path integral partition functions is an important way of deriving the thermodynamical properties of black holes. However, there are certain black hole models and some mathematically analog mechanical models for which this method cannot be applied directly. This is due to the fact that their action evaluated on a classical solution is not finite and its first variation does not vanish for all consistent boundary conditions. These problems can be dealt with by adding a counterterm to the classical action, which is a solution of the corresponding Hamilton-Jacobi equation. In this work we study the effects of polymer quantization on a mechanical model presenting the aforementioned difficulties and contrast it with the above counterterm method. This type of quantization for mechanical models is motivated by the loop quantization of gravity, which is known to play a role in the thermodynamics of black hole systems. The model we consider is a nonrelativistic particle in an inverse square potential, and we analyze two polarizations of the polymer quantization in which either the position or the momentum is discrete. In the former case, Thiemann's regularization is applied to represent the inverse power potential, but we still need to incorporate the Hamilton-Jacobi counterterm, which is now modified by polymer corrections. In the latter, momentum discrete case, however, such regularization could not be implemented. Yet, remarkably, owing to the fact that the position is bounded, we do not need a Hamilton-Jacobi counterterm in order to have a well-defined saddle point approximation. Further developments and extensions are commented upon in the discussion.
Inverse structure functions in the canonical wind turbine array boundary layer
Viggiano, Bianca; Gion, Moira; Ali, Naseem; Tutkun, Murat; Cal, Raúl Bayoán
2015-11-01
Insight into the statistical behavior of the flow past an array of wind turbines is useful in determining how to improve power extraction from the overall available energy. Considering a wind tunnel experiment, hot-wire anemometer velocity signals are obtained at the centerline of a 3 x 3 canonical wind turbine array boundary layer. Two downstream locations are considered referring to the near- and far-wake, and 21 vertical points were acquired per profile. Velocity increments are used to quantify the ordinary and inverse structure functions at both locations and their relationship between the scaling exponents is noted. It is of interest to discern if there is evidence of an inverted scaling. The inverse structure functions will also be discussed from the standpoint of the proximity to the array. Observations will also address if inverted scaling exponents follow a power law behavior and furthermore, extended self-similarity of the second moment is used to obtain the scaling exponent of other moments. Inverse structure functions of moments one through eight are tested via probability density functions and the behavior of the negative moment is investigated as well. National Science Foundation-CBET-1034581.
Creativity and Brain-Functioning in Product Development Engineers: A Canonical Correlation Analysis
Travis, Frederick; Lagrosen, Yvonne
2014-01-01
This study used canonical correlation analysis to explore the relation among scores on the Torrance test of figural and verbal creativity and demographic, psychological and physiological measures in Swedish product-development engineers. The first canonical variate included figural and verbal flexibility and originality as dependent measures and…
Partition and Correlation Functions of a Freely Crossed Network Using Ising Model-Type Interactions
Saito, Akira
2016-01-01
We set out to determine the partition and correlation functions of a network under the assumption that its elements are freely connected, with an Ising model-type interaction energy associated with each connection. The partition function is obtained from all combinations of loops on the free network, while the correlation function between two elements is obtained based on all combinations of routes between these points, as well as all loops on the network. These functions allow measurement of the dynamics over the whole of any network, regardless of its form. Furthermore, even as parts are added to the network, the partition and correlation functions can still be obtained. As an example, we obtain the partition and correlation functions in a crystal system under the repeated addition of fixed parts.
Recursive method for the Nekrasov partition function for classical Lie groups
International Nuclear Information System (INIS)
The Nekrasov partition function for supersymmetric gauge theories with general Lie groups is, so far, not known in a closed form, while there is a definition in terms of the integral. In this paper, as an intermediate step to derive the closed form, we give a recursion formula among partition functions, which can be derived from the integral. We apply the method to a toy model that reflects the basic structure of partition functions for BCD-type Lie groups and obtain a closed expression for the factor associated with the generalized Young diagram
Relations between canonical and non-canonical inflation
Energy Technology Data Exchange (ETDEWEB)
Gwyn, Rhiannon [Max-Planck-Institut fuer Gravitationsphysik (Albert-Einstein-Institut), Potsdam (Germany); Rummel, Markus [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik; Westphal, Alexander [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany). Theory Group
2012-12-15
We look for potential observational degeneracies between canonical and non-canonical models of inflation of a single field {phi}. Non-canonical inflationary models are characterized by higher than linear powers of the standard kinetic term X in the effective Lagrangian p(X,{phi}) and arise for instance in the context of the Dirac-Born-Infeld (DBI) action in string theory. An on-shell transformation is introduced that transforms non-canonical inflationary theories to theories with a canonical kinetic term. The 2-point function observables of the original non-canonical theory and its canonical transform are found to match in the case of DBI inflation.
Relations between canonical and non-canonical inflation
International Nuclear Information System (INIS)
We look for potential observational degeneracies between canonical and non-canonical models of inflation of a single field φ. Non-canonical inflationary models are characterized by higher than linear powers of the standard kinetic term X in the effective Lagrangian p(X,φ) and arise for instance in the context of the Dirac-Born-Infeld (DBI) action in string theory. An on-shell transformation is introduced that transforms non-canonical inflationary theories to theories with a canonical kinetic term. The 2-point function observables of the original non-canonical theory and its canonical transform are found to match in the case of DBI inflation.
On partition function and Weyl anomaly of conformal higher-spin fields
International Nuclear Information System (INIS)
We study 4-dimensional higher-derivative conformal higher-spin (CHS) fields generalizing Weyl graviton and conformal gravitino. They appear, in particular, as “induced” theories in the AdS/CFT context. We consider their partition function on curved Einstein-space backgrounds like (A)dS or sphere and Ricci-flat spaces. Remarkably, the bosonic (integer spin s) CHS partition function appears to be given by a product of partition functions of the standard 2nd-derivative “partially massless” spin s fields, generalizing the previously known expression for the 1-loop Weyl graviton (s=2) partition function. We compute the corresponding spin s Weyl anomaly coefficients as and cs. Our result for as reproduces the expression found recently in (arXiv:1306.5242) by an indirect method implied by AdS/CFT (which relates the partition function of a CHS field on S4 to a ratio of known partition functions of massless higher-spin field in AdS5 with alternate boundary conditions). We also obtain similar results for the fermionic CHS fields. In the half-integer s case the CHS partition function on (A)dS background is given by the product of squares of “partially massless” spin s partition functions and one extra factor corresponding to a special massive conformally invariant spin s field. It was noticed in (arXiv:1306.5242) that the sum of the bosonic as coefficients over all s is zero when computed using the ζ-function regularization, and we observe that the same property is true also in the fermionic case
One-loop partition function of three-dimensional flat gravity
Barnich, Glenn; Gonzalez, Hernan A.; Maloney, Alexander; Oblak, Blagoje
2015-01-01
In this note we point out that the one-loop partition function of three-dimensional flat gravity, computed along the lines originally developed for the anti-de Sitter case, reproduces characters of the BMS3 group.
On the domain wall partition functions of level-1 affine so(n) vertex models
Dow, A.; Foda, O.
2006-01-01
We derive determinant expressions for domain wall partition functions of level-1 affine so(n) vertex models, n >= 4, at discrete values of the crossing parameter lambda = m pi / 2(n-3), m in Z, in the critical regime.
A paradox in the electronic partition function or how to be cautious with mathematics
International Nuclear Information System (INIS)
When the electronic partition functions of atoms or molecules are evaluated in textbooks, only the contribution of the ground state is considered. The excited states' contribution is argued to be negligible. However, a closer look shows that the partition function diverges if such states are taken into account. This paper shows that the blind use of mathematics is the reason behind this odd behaviour. (author)
Partition function zeros at first-order phase transitions: A general analysis
Biskup, Marek; Borgs, Christian; Chayes, Jennifer T.; Kleinwaks, Logan J.; Kotecky, Roman
2003-01-01
We present a general, rigorous theory of partition function zeros for lattice spin models depending on one complex parameter. First, we formulate a set of natural assumptions which are verified for a large class of spin models in a companion paper [BBCKK2, math-ph/0304007]. Under these assumptions, we derive equations whose solutions give the location of the zeros of the partition function with periodic boundary conditions, up to an error which we prove is (generically) exponentially small in...
On the analytical evaluation of the partition function for unit hypercubes in four dimensions
International Nuclear Information System (INIS)
The group integrations required for the analytic evaluation of the partition function for unit hypercubes in four dimensions are carried out. Modifications of the graphical rules for SU2 group integrations cited in the literature are developed for this purpose. A complete classification of all surfaces that can be embedded in the unit hypercube is given and their individual contribution to the partition function worked out. Applications are discussed briefly. (orig.)
The partition function of the trigonometric SOS model with a reflecting end
International Nuclear Information System (INIS)
We compute the partition function of the trigonometric SOS model with one reflecting end and domain wall type boundary conditions. We show that in this case, instead of the sum of determinants obtained by Rosengren for the SOS model on a square lattice without reflection, the partition function can be represented as a single Izergin determinant. This result is crucial for the study of the Bethe vectors of the spin chains with non-diagonal boundary terms. (letter)
LETTER: The partition function of the trigonometric SOS model with a reflecting end
Filali, G.; Kitanine, N.
2010-06-01
We compute the partition function of the trigonometric SOS model with one reflecting end and domain wall type boundary conditions. We show that in this case, instead of the sum of determinants obtained by Rosengren for the SOS model on a square lattice without reflection, the partition function can be represented as a single Izergin determinant. This result is crucial for the study of the Bethe vectors of the spin chains with non-diagonal boundary terms.
Computing the partition function for perfect matchings in a hypergraph
Barvinok, Alexander
2010-01-01
Given non-negative weights w_S on the k-subsets S of a km-element set V, we consider the sum of the products w_{S_1} ... w_{S_m} for all partitions V = S_1 cup ... cup S_m into pairwise disjoint k-subsets S_i. When the weights w_S are positive and within a constant factor, fixed in advance, of each other, we present a simple polynomial time algorithm to approximate the sum within a polynomial in m factor. In the process, we obtain higher-dimensional versions of the van der Waerden and Bregman-Minc bounds for permanents.
One loop partition function in AdS_3/CFT_2
Chen, Bin
2015-01-01
The 1-loop partition function of the handle-body solutions in the AdS$_3$ gravity have been derived some years ago using the heat-kernel and the method of images. In the semiclassical limit, such partition function should correspond to the order $O (c^0)$ part in the partition function of dual conformal field theory on the boundary Riemann surface. The higher genus partition function could be computed by the multi-point functions in the Riemann sphere via sewing prescription. In the large central charge limit, to the leading order of $c$, the multi-point function is further simplified to be a summation over the product of two-point functions, which may form links. Each link is in one-to-one correspondence with the conjugacy class of the Schottky group of the Riemann surface. Moreover, the value of a link is determined by the eigenvalue of the element in the conjugate class. This allows us to reproduce exactly the gravitational 1-loop partition function. The proof can be generalized to the higher spin gravity ...
Wigner expansions for partition functions of nonrelativistic and relativistic oscillator systems
Zylka, Christian; Vojta, Guenter
1993-01-01
The equilibrium quantum statistics of various anharmonic oscillator systems including relativistic systems is considered within the Wigner phase space formalism. For this purpose the Wigner series expansion for the partition function is generalized to include relativistic corrections. The new series for partition functions and all thermodynamic potentials yield quantum corrections in terms of powers of h(sup 2) and relativistic corrections given by Kelvin functions (modified Hankel functions) K(sub nu)(mc(sup 2)/kT). As applications, the symmetric Toda oscillator, isotonic and singular anharmonic oscillators, and hindered rotators, i.e. oscillators with cosine potential, are addressed.
Ising model on random networks and the canonical tensor model
International Nuclear Information System (INIS)
We introduce a statistical system on random networks of trivalent vertices for the purpose of studying the canonical tensor model, which is a rank-three tensor model in the canonical formalism. The partition function of the statistical system has a concise expression in terms of integrals, and has the same symmetries as the kinematical ones of the canonical tensor model. We consider the simplest non-trivial case of the statistical system corresponding to the Ising model on random networks, and find that its phase diagram agrees with what is implied by regrading the Hamiltonian vector field of the canonical tensor model with N=2 as a renormalization group flow. Along the way, we obtain an explicit exact expression of the free energy of the Ising model on random networks in the thermodynamic limit by the Laplace method. This paper provides a new example connecting a model of quantum gravity and a random statistical system
Nagesh, Jayashree; Brumer, Paul; Izmaylov, Artur F
2016-01-01
We extend the localized operator partitioning method (LOPM) [J. Nagesh, A.F. Izmaylov, and P. Brumer, J. Chem. Phys. 142, 084114 (2015)] to the time-dependent density functional theory (TD-DFT) framework to partition molecular electronic energies of excited states in a rigorous manner. A molecular fragment is defined as a collection of atoms using Stratman-Scuseria-Frisch atomic partitioning. A numerically efficient scheme for evaluating the fragment excitation energy is derived employing a resolution of the identity to preserve standard one- and two-electron integrals in the final expressions. The utility of this partitioning approach is demonstrated by examining several excited states of two bichromophoric compounds: 9-((1-naphthyl)-methyl)-anthracene and 4-((2-naphthyl)-methyl)-benzaldehyde. The LOPM is found to provide nontrivial insights into the nature of electronic energy localization that are not accessible using simple density difference analysis.
You, Setthivoine
2015-11-01
A new canonical field theory has been developed to help interpret the interaction between plasma flows and magnetic fields. The theory augments the Lagrangian of general dynamical systems to rigourously demonstrate that canonical helicity transport is valid across single particle, kinetic and fluid regimes, on scales ranging from classical to general relativistic. The Lagrangian is augmented with two extra terms that represent the interaction between the motion of matter and electromagnetic fields. The dynamical equations can then be re-formulated as a canonical form of Maxwell's equations or a canonical form of Ohm's law valid across all non-quantum regimes. The field theory rigourously shows that helicity can be preserved in kinetic regimes and not only fluid regimes, that helicity transfer between species governs the formation of flows or magnetic fields, and that helicity changes little compared to total energy only if density gradients are shallow. The theory suggests a possible interpretation of particle energization partitioning during magnetic reconnection as canonical wave interactions. This work is supported by US DOE Grant DE-SC0010340.
Iterating free-field AdS/CFT: higher spin partition function relations
Beccaria, Matteo; Tseytlin, Arkady A.
2016-07-01
We find a simple relation between a free higher spin partition function on the thermal quotient of {{AdS}}d+1 and the partition function of the associated d-dimensional conformal higher spin field defined on the thermal quotient of {{AdS}}d. Starting with a conformal higher spin field defined in {{AdS}}d, one may also associate to with another conformal field in d-1 dimensions, thus iterating AdS/CFT. We observe that in the case of d=4, this iteration leads to a trivial 3d higher spin conformal theory with parity-even non-local action: it describes a zero total number of dynamical degrees of freedom and the corresponding partition function is equal to 1.
Canonical quantization of macroscopic electromagnetism
Philbin, Thomas Gerard
2010-01-01
Application of the standard canonical quantization rules of quantum field theory to macroscopic electromagnetism has encountered obstacles due to material dispersion and absorption. This has led to a phenomenological approach to macroscopic quantum electrodynamics where no canonical formulation is attempted. In this paper macroscopic electromagnetism is canonically quantized. The results apply to any linear, inhomogeneous, magnetodielectric medium with dielectric functions that obey the Krame...
A Unified Scheme for Modular Invariant Partition Functions of WZW Models
Abolhassani, M R
1994-01-01
We introuduce a unified method which can be applied to any WZW model at arbitrary level to search systematically for modular invariant physical partition functions. Our method is based essentially on modding out a known theory on group manifold $G$ by a discrete group $\\Gamma$. We apply our method to $\\widehat {su(n)}$ with $n=2,3,4,5,6$, and to $\\widehat {g_2}$ models, and obtain all the known partition functions and some new ones, and give explicit expressions for all of them.
Partition Functions for Diatomic Molecules in Plasmas out of Thermal Equilibrium
Institute of Scientific and Technical Information of China (English)
Geraldine FAURE
2012-01-01
Two calculation methods on the partition functions for diatomic molecules in plas- mas out of thermal equilibrium are reported. A Boltzmann distribution for the electronic, vi- brational and rotational quantum levels is assumed in the two calculation methods. The results obtained by two methods are displayed for four sorts of diatomic molecules, 02, N2, OH and NO, that are present in humid air plasmas. The calculation method of density for the electronically excited states is developed. Finally, a method to calculate the partition functions for simulating the non-normalized diatomic spectra is discussed.
Functional Selectivity of CB2 Cannabinoid Receptor Ligands at a Canonical and Noncanonical Pathway.
Dhopeshwarkar, Amey; Mackie, Ken
2016-08-01
The CB2 cannabinoid receptor (CB2) remains a tantalizing, but unrealized therapeutic target. CB2 receptor ligands belong to varied structural classes and display extreme functional selectivity. Here, we have screened diverse CB2 receptor ligands at canonical (inhibition of adenylyl cyclase) and noncanonical (arrestin recruitment) pathways. The nonclassic cannabinoid (-)-cis-3-[2-hydroxy-4-(1,1-dimethylheptyl)phenyl]-trans-4-(3-hydroxypropyl)cyclohexanol (CP55940) was the most potent agonist for both pathways, while the classic cannabinoid ligand (6aR,10aR)-3-(1,1-Dimethylbutyl)-6a,7,10,10a-tetrahydro-6,6,9-trimethyl-6H-dibenzo[b,d]pyran JWH133) was the most efficacious agonist among all the ligands profiled in cyclase assays. In the cyclase assay, other classic cannabinoids showed little [(-)-trans-Δ(9)-tetrahydrocannabinol and (-)-(6aR,7,10,10aR)-tetrahydro-6,6,9-trimethyl-3-(1-methyl-1-phenylethyl)-6H-dibenzo[b,d]pyran-1-ol] (KM233) to no efficacy [(6aR,10aR)-1-methoxy-6,6,9-trimethyl-3-(2-methyloctan-2-yl)-6a,7,10,10a-tetrahydrobenzo[c]chromene(L759633) and (6aR,10aR)-3-(1,1-dimethylheptyl)-6a,7,8,9,10,10a-hexahydro-1-methoxy-6,6-dimethyl-9-methylene-6H-dibenzo[b,d]pyran]L759656. Most aminoalkylindoles, including [(3R)-2,3-dihydro-5-methyl-3-(4-morpholinylmethyl)pyrrolo[1,2,3-de]-1,4-benzoxazin-6-yl]-1-naphthalenyl-methanone, monomethanesulfonate (WIN55212-2), were moderate efficacy agonists. The cannabilactone 3-(1,1-dimethyl-heptyl)-1-hydroxy-9-methoxy-benzo(c)chromen-6-one (AM1710) was equiefficacious to CP55940 to inhibit adenylyl cyclase, albeit with lower potency. In the arrestin recruitment assays, all classic cannabinoid ligands failed to recruit arrestins, indicating a bias toward G-protein coupling for this class of compound. All aminoalkylindoles tested, except for WIN55212-2 and (1-pentyl-1H-indol-3-yl)(2,2,3,3-tetramethylcyclopropyl)-methanone (UR144), failed
Partitioning heritability by functional category using GWAS summary statistics
DEFF Research Database (Denmark)
Finucane, Hilary K.; Bulik-Sullivan, Brendan; Gusev, Alexander;
2015-01-01
Recent work has demonstrated that some functional categories of the genome contribute disproportionately to the heritability of complex diseases. Here we analyze a broad set of functional elements, including cell type–specific elements, to estimate their polygenic contributions to heritability in...... type–specific enrichments, including significant enrichment of central nervous system cell types in the heritability of body mass index, age at menarche, educational attainment and smoking behavior....
Partitioning of minimotifs based on function with improved prediction accuracy.
Directory of Open Access Journals (Sweden)
Sanguthevar Rajasekaran
Full Text Available BACKGROUND: Minimotifs are short contiguous peptide sequences in proteins that are known to have a function in at least one other protein. One of the principal limitations in minimotif prediction is that false positives limit the usefulness of this approach. As a step toward resolving this problem we have built, implemented, and tested a new data-driven algorithm that reduces false-positive predictions. METHODOLOGY/PRINCIPAL FINDINGS: Certain domains and minimotifs are known to be strongly associated with a known cellular process or molecular function. Therefore, we hypothesized that by restricting minimotif predictions to those where the minimotif containing protein and target protein have a related cellular or molecular function, the prediction is more likely to be accurate. This filter was implemented in Minimotif Miner using function annotations from the Gene Ontology. We have also combined two filters that are based on entirely different principles and this combined filter has a better predictability than the individual components. CONCLUSIONS/SIGNIFICANCE: Testing these functional filters on known and random minimotifs has revealed that they are capable of separating true motifs from false positives. In particular, for the cellular function filter, the percentage of known minimotifs that are not removed by the filter is approximately 4.6 times that of random minimotifs. For the molecular function filter this ratio is approximately 2.9. These results, together with the comparison with the published frequency score filter, strongly suggest that the new filters differentiate true motifs from random background with good confidence. A combination of the function filters and the frequency score filter performs better than these two individual filters.
Drinfeld twist and the domain wall partition function of the eight-vertex model
Institute of Scientific and Technical Information of China (English)
Hao Kun; Chen xi; Shi Kang-Jie; Yang Wen-Li
2011-01-01
With the help of the F-basis provided by the Drinfeld twist or factorising F-matrix for the spatial optical soliton model associated with the eight-vertex model, we calculate the partition function for the eight-vertex model on an N × N square lattice with domain wall boundary condition.
On the Definition of the Partition Function in Quantum Regge Calculus
Nishimura, Jun(Department, of, Particle, and, Nuclear, Physics,, Graduate, University, for, Advanced, Studies, (SOKENDAI),, Tsukuba,, Ibaraki, 305-0801,, Japan)
1995-01-01
We argue that the definition of the partition function used recently to demonstrate the failure of Regge calculus is wrong. In fact, in the one-dimensional case, we show that there is a more natural definition, with which one can reproduce the correct results.
5D partition functions, q-Virasoro systems and integrable spin-chains
Nieri, Fabrizio; Passerini, Filippo; Torrielli, Alessandro
2013-01-01
We analyze N = 1 theories on S5 and S4 x S1, showing how their partition functions can be written in terms of a set of fundamental 5d holomorphic blocks. We demonstrate that, when the 5d mass parameters are analytically continued to suitable values, the S5 and S4 x S1 partition functions degenerate to those for S3 and S2 x S1. We explain this mechanism via the recently proposed correspondence between 5d partition functions and correlators with underlying q-Virasoro symmetry. From the q-Virasoro 3-point functions, we axiomatically derive a set of associated reflection coefficients, and show they can be geometrically interpreted in terms of Harish-Chandra c-functions for quantum symmetric spaces. We then link these particular c-functions to the types appearing in the Jost functions encoding the asymptotics of the scattering in integrable spin chains, obtained taking different limits of the XYZ model to XXZ-type.
Partition functions for quantum gravity, black holes, elliptic genera and Lie algebra homologies
International Nuclear Information System (INIS)
There is a remarkable connection between quantum generating functions of field theory and formal power series associated with dimensions of chains and homologies of suitable Lie algebras. We discuss the homological aspects of this connection with its applications to partition functions of the minimal three-dimensional gravities in the space-time asymptotic to AdS3, which also describe the three-dimensional Euclidean black holes, the pure N=1 supergravity, and a sigma model on N-fold generalized symmetric products. We also consider in the same context elliptic genera of some supersymmetric sigma models. These examples can be considered as a straightforward application of the machinery of modular forms and spectral functions (with values in the congruence subgroup of SL(2,Z)) to partition functions represented by means of formal power series that encode Lie algebra properties.
A Partitioned Correlation Function Interaction approach for describing electron correlation in atoms
Verdebout, S; Jönsson, P; Gaigalas, G; Fischer, C Froese; Godefroid, M
2013-01-01
Traditional multiconfiguration Hartree-Fock (MCHF) and configuration interaction (CI) methods are based on a single orthonormal orbital basis (OB). For atoms with complicated shell structures, a large OB is needed to saturate all the electron correlation effects. The large OB leads to massive configuration state function (CSF) expansions that are difficult to handle. We show that it is possible to relax the orthonormality restriction on the OB and break down the originally large calculations to a set of smaller ones that can be run in parallel. Each calculation determines a partitioned correlation function (PCF) that accounts for a specific correlation effect. The PCFs are built on optimally localized orbital sets and are added to a zero-order multireference (MR) function to form a total wave function. The mixing coefficients of the PCFs are fixed from a small generalized eigenvalue problem. The required matrices are computed using a biorthonormal transformation technique. The new method, called partitioned c...
Chikkagoudar, Satish; Roshan, Usman; Livesay, Dennis
2007-01-01
Probalign computes maximal expected accuracy multiple sequence alignments from partition function posterior probabilities. To date, Probalign is among the very best scoring methods on the BAliBASE, HOMSTRAD and OXBENCH benchmarks. Here, we introduce eProbalign, which is an online implementation of the approach. Moreover, the eProbalign web server doubles as an online platform for post-alignment analysis. The heart-and-soul of the post-alignment functionality is the Probalign Alignment Viewer ...
Alcaraz-Pérez, Francisca; García-Castillo, Jesús; García-Moreno, Diana; López-Muñoz, Azucena; Anchelin, Monique; Angosto, Diego; Zon, Leonard I.; Mulero, Victoriano; Cayuela, María L.
2014-02-01
Dyskeratosis congenita (DC) is an inherited disorder with mutations affecting telomerase or telomeric proteins. DC patients usually die of bone marrow failure. Here we show that genetic depletion of the telomerase RNA component (TR) in the zebrafish results in impaired myelopoiesis, despite normal development of haematopoietic stem cells (HSCs). The neutropenia caused by TR depletion is independent of telomere length and telomerase activity. Genetic analysis shows that TR modulates the myeloid-erythroid fate decision by controlling the levels of the master myeloid and erythroid transcription factors spi1 and gata1, respectively. The alteration in spi1 and gata1 levels occurs through stimulation of gcsf and mcsf. Our model of TR deficiency in the zebrafish illuminates the non-canonical roles of TR, and could establish therapeutic targets for DC.
Semenov, Alexander; Zaikin, Oleg
2016-01-01
In this paper we propose an approach for constructing partitionings of hard variants of the Boolean satisfiability problem (SAT). Such partitionings can be used for solving corresponding SAT instances in parallel. For the same SAT instance one can construct different partitionings, each of them is a set of simplified versions of the original SAT instance. The effectiveness of an arbitrary partitioning is determined by the total time of solving of all SAT instances from it. We suggest the approach, based on the Monte Carlo method, for estimating time of processing of an arbitrary partitioning. With each partitioning we associate a point in the special finite search space. The estimation of effectiveness of the particular partitioning is the value of predictive function in the corresponding point of this space. The problem of search for an effective partitioning can be formulated as a problem of optimization of the predictive function. We use metaheuristic algorithms (simulated annealing and tabu search) to move from point to point in the search space. In our computational experiments we found partitionings for SAT instances encoding problems of inversion of some cryptographic functions. Several of these SAT instances with realistic predicted solving time were successfully solved on a computing cluster and in the volunteer computing project SAT@home. The solving time agrees well with estimations obtained by the proposed method. PMID:27190753
Missing mass approximations for the partition function of stimulus driven Ising models.
Haslinger, Robert; Ba, Demba; Galuske, Ralf; Williams, Ziv; Pipa, Gordon
2013-01-01
Ising models are routinely used to quantify the second order, functional structure of neural populations. With some recent exceptions, they generally do not include the influence of time varying stimulus drive. Yet if the dynamics of network function are to be understood, time varying stimuli must be taken into account. Inclusion of stimulus drive carries a heavy computational burden because the partition function becomes stimulus dependent and must be separately calculated for all unique stimuli observed. This potentially increases computation time by the length of the data set. Here we present an extremely fast, yet simply implemented, method for approximating the stimulus dependent partition function in minutes or seconds. Noting that the most probable spike patterns (which are few) occur in the training data, we sum partition function terms corresponding to those patterns explicitly. We then approximate the sum over the remaining patterns (which are improbable, but many) by casting it in terms of the stimulus modulated missing mass (total stimulus dependent probability of all patterns not observed in the training data). We use a product of conditioned logistic regression models to approximate the stimulus modulated missing mass. This method has complexity of roughly O(LNNpat) where is L the data length, N the number of neurons and N pat the number of unique patterns in the data, contrasting with the O(L2 (N) ) complexity of alternate methods. Using multiple unit recordings from rat hippocampus, macaque DLPFC and cat Area 18 we demonstrate our method requires orders of magnitude less computation time than Monte Carlo methods and can approximate the stimulus driven partition function more accurately than either Monte Carlo methods or deterministic approximations. This advance allows stimuli to be easily included in Ising models making them suitable for studying population based stimulus encoding. PMID:23898262
Missing Mass Approximations for the Partition Function of Stimulus Driven Ising Models
Directory of Open Access Journals (Sweden)
Robert Haslinger
2013-07-01
Full Text Available Ising models are routinely used to quantify the second order, functional structure of neural populations. With some recent exceptions, they generally do not include the influence of time varying stimulus drive. Yet if the dynamics of network function are to be understood, time varying stimuli must be taken into account. Inclusion of stimulus drive carries a heavy computational burden because the partition function becomes stimulus dependent and must be separately calculated for all unique stimuli observed. This potentially increases computation time by the length of the data set. Here we present an extremely fast, yet simply implemented, method for approximating the stimulus dependent partition function in minutes or seconds. Noting that the most probable spike patterns (which are few occur in the training data, we sum partition function terms corresponding to those patterns explicitly. We then approximate the sum over the remaining patterns (which are improbable, but many by casting it in terms of the stimulus modulated missing mass (total stimulus dependent probability of all patterns not observed in the training data. We use use a product of conditioned logistic regression models to approximate the stimulus modulated missing mass. This method has complexity of roughly O(LNN_{pat} where is L the data length, N the number of neurons and N_{pat} the number of unique patterns in the data, contrasting with the O(L2^N complexity of alternate methods. Using multiple unit recordings from rat hippocampus, macaque DLPFC and cat Area 18 we demonstrate our method requires orders of magnitude less computation time than Monte Carlo methods and can approximate the stimulus driven partition function more accurately than either Monte Carlo methods or deterministic approximations. This advance allows stimuli to be easily included in Ising models making them suitable for studying population based stimulus encoding.
The method of evaluating quantum partition function for the Hubbard model
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The method of evaluation of quantum partition function (QPF) in some four fermion models is proposed. The calculations are carried out by the path integral method. The integral is evaluated by introducing the additional fields (called Hubbard-Stratanovich transformation in some models), integration over fermionic variables, and considering the finite-dimensional approximation of rest integral over bosonic fields in the infinite limit. The result can be represented as a sum of the functional derivatives with respect to the arbitrary bosonic field of the quantum partition of free fermionic theory in the external bosonic field. This expression can be treated in a mean field approximation in closed form (the determinants corresponding to the arbitrary external field are substituted by its mean values corresponding to the mean value of the external fields). The quantum partition function is represented as the integral representation of the function. The approximation for the QPF of the free theory is considered, and the corresponding answer for QPF is studied. A convenient perturbation expansion for ln Z is developed. (author). 6 refs, 1 fig
Heat capacity decomposition by partition function zeros for interacting self-avoiding walks
Chen, Chi-Ning; Hsieh, Yu-Hsin; Hu, Chin-Kun
2013-10-01
A novel method based on partition function zeros is developed to demonstrate the additional advantages by considering both loci of partition function zeros and thermodynamical functions associated with them. With this method, the first pair of complex conjugate zeros (first zeros) can be defined without ambiguity and the critical point of a small system can be defined as the peak position of the heat capacity component associated with the first zeros. For the system with two phase transitions, two pairs of first zeros corresponding to two phase transitions can be identified and two overlapping phase transitions can be well separated. This method is applied to the interacting self-avoiding walk (ISAW) of homopolymer with N monomers on the simple cubic lattice, which has a collapse transition at a higher temperature and a freezing transition at a low temperature. The exact partition functions ZN with N up to 27 are calculated and our approach gives a clear scenario for the collapse and the freezing transitions.
Partition function of N=2* SYM on a large four-sphere
Hollowood, Timothy J
2015-01-01
We examine the partition function of N=2* supersymmetric SU(N) Yang-Mills theory on the four-sphere in the large radius limit. We point out that the large radius partition function, at fixed N, is computed by saddle points lying on particular walls of marginal stability on the Coulomb branch of the theory on R^4. For N an even (odd) integer and \\theta_YM=0, (\\pi), these include a point of maximal degeneration of the Donagi-Witten curve to a torus where BPS dyons with electric charge [N/2] become massless. We argue that the dyon singularity is the lone saddle point in the SU(2) theory, while for SU(N) with N>2, we characterize potentially competing saddle points by obtaining the relations between the Seiberg-Witten periods at such points. Using Nekrasov's instanton partition function, we solve for the maximally degenerate saddle point and obtain its free energy as a function of g_YM and N, and show that the results are "large-N exact". In the large-N theory our results provide analytical expressions for the pe...
Barklem, Paul S
2016-01-01
Partition functions and dissociation equilibrium constants are presented for 291 diatomic molecules for temperatures in the range from near absolute zero to 10000 K, thus providing data for many diatomic molecules of astrophysical interest at low temperature. The calculations are based on molecular spectroscopic data from the book of Huber and Herzberg with significant improvements from the literature, especially updated data for ground states of many of the most important molecules by Irikura. Dissociation energies are collated from compilations of experimental and theoretical values. Partition functions for 284 species of atoms for all elements from H to U are also presented based on data collected at NIST. The calculated data are expected to be useful for modelling a range of low density astrophysical environments, especially star-forming regions, protoplanetary disks, the interstellar medium, and planetary and cool stellar atmospheres. The input data, which will be made available electronically, also prov...
The 2-loop partition function of large N gauge theories with adjoint matter on S^3
Mussel, Matan
2009-01-01
We compute the 2-loop thermal partition function of Yang-Mills theory on a small 3-sphere, in the large N limit with weak 't Hooft coupling. We include N_s scalars and N_f chiral fermions in the adjoint representation of the gauge group (S)U(N), with arbitrary Yukawa and quartic scalar couplings, assuming only commutator interactions. From this computation one can extract information on the perturbative corrections to the spectrum of the theory, and the correction to its Hagedorn temperature. Furthermore, the computation of the 2-loop partition function is a necessary step towards determining the order of the deconfinement phase transition at weak coupling, for which a 3-loop computation is needed.
International Nuclear Information System (INIS)
We construct polarized spin reversal operator (PSRO) which yields a class of representations for the BCN type of Weyl algebra, and subsequently use this PSRO to find out novel exactly solvable variants of the BCN type of spin Calogero model. The strong coupling limit of such spin Calogero models generates the BCN type of Polychronakos spin chains with PSRO. We derive the exact spectra of the BCN type of spin Calogero models with PSRO and compute the partition functions of the related spin chains by using the freezing trick. We also find out an interesting relation between the partition functions of the BCN type and AN−1 type of Polychronakos spin chains. Finally, we study spectral properties like level density and distribution of spacing between consecutive energy levels for BCN type of Polychronakos spin chains with PSRO
Taormina, Anne
1993-05-01
The representation theory of the doubly extended N=4 superconformal algebra is reviewed. The modular properties of the corresponding characters can be derived, using characters sumrules for coset realizations of these N=4 algebras. Some particular combinations of massless characters are shown to transform as affine SU(2) characters under S and T, a fact used to completely classify the massless sector of the partition function.
An axiomatic characterization of a value for games in partition function form
Hu, Cheng-Cheng; Yang, Yi-You
2010-01-01
An extension of the Shapley value for games in partition function form is proposed in the paper. We introduce a version of the marginal contributions for environments with externalities. The dummy property related to it is defined. We adapt the system of axioms provided by Shapley (A value for n-Person games. In: Kuhn H, Tucker A (eds) Contributions to the theory of games II. Princeton University Press, Princeton, pp 307317, 1953) to characterize our value. In addition, we discuss a relations...
Abroi, Aare; Ilves, Ivar; Kivi, Sirje; Ustav, Mart
2004-02-01
Recent studies have suggested that the tethering of viral genomes to host cell chromosomes could provide one of the ways to achieve their nuclear retention and partitioning during extrachromosomal maintenance in dividing cells. The data we present here provide firm evidence that the partitioning of the bovine papillomavirus type 1 (BPV1) genome is dependent on the chromatin attachment process mediated by viral E2 protein and its multiple binding sites. On the other hand, the attachment of E2 and the E2-mediated tethering of reporter plasmids to host chromosomes are not necessarily sufficient for efficient partitioning, suggesting that additional E2-dependent activities might be involved in the latter process. The activity of E2 protein in chromatin attachment and partitioning is more sensitive to the point mutations in the N-terminal domain than its transactivation and replication initiation functions. Therefore, at least part of the interactions of the E2 N-terminal domain with its targets during the chromatin attachment and partitioning processes are likely to involve specific receptors not involved in transactivation and replication activities of the protein. The mutational analysis also indicates that the binding of E2 to chromatin is not achieved through interaction of linear N-terminal subsequences of the E2 protein with putative receptors. Instead, the composite surface elements of the N-terminal domain build up the receptor-binding surface of E2. In this regard, the interaction of BPV1 E2 with its chromosomal targets clearly differs from the interactions of LANA1 protein from Kaposi's sarcoma-associated human herpesvirus and EBNA1 from Epstein-Barr virus with their specific receptors. PMID:14747575
International Nuclear Information System (INIS)
By means of the semiempirical quantum chemical MINDO/3- and MNDO-MO-methods it is possible to perform calculations for use in evaluation or interpretation of isotope effects to such an extent that would not be rationally fossible by corresponding experiments. But only the calculated reduced partition function ratios of isotopically substituted molecules can be applied with sufficient reliability for discussions. The temperature dependence of the reduced partition function ratios of over 100 molecules, ions, and radicals regarding the H/D, 12C/13C-, 14N/15N-, 16O/18O-, 28Si/30Si-, 32S/34S-, and 35Cl/37Cl-substitution has been calculated. From these results general conclusions concerning the dependence of isotope effects from the chemical structure of the corresponding molecules have been drawn. In particular, a relationship between the reduced partition function ratio and the electronic charge of the substituted atom has been found. In addition, examples are given for the application of the calculation algorithm used above in connection with combined isotopic substitutions, radical cations, and transition states of chemical reactions. (author)
Geometry of Spin and Spin^c structures in the M-theory partition function
Sati, Hisham
2010-01-01
We study the effects of having multiple Spin structures on the partition function of the spacetime fields in M-theory. This leads to a potential anomaly which appears in the eta-invariants upon variation of the Spin structure. The main source of such spaces are manifolds with nontrivial fundamental group, which are also important in realistic models. We extend the discussion to the Spin^c case and find the phase of the partition function, and revisit the quantization condition for the C-field in this case. In type IIA string theory in ten dimensions, the mod 2 index of the Dirac operator is the obstruction to having a well-defined partition function. We geometrically characterize manifolds with and without such an anomaly and extend to the case of nontrivial fundamental group. The lift to KO-theory gives the alpha-invariant, which in general depends on the Spin structure. This reveals many interesting connection to positive scalar curvature manifolds and constructions related to the Gromov-Lawson(-Rosenberg) ...
Mcconaghy, Trent; Gielen, Georges
2011-01-01
This paper presents a method to automatically generate compact symbolic performance models of analog circuits with no prior specification of an equation template. The approach takes SPICE simulation data as input, which enables modeling of any nonlinear circuits and circuit characteristics. Genetic programming is applied as a means of traversing the space of possible symbolic expressions. A grammar is specially designed to constrain the search to a canonical form for functions. Novel evolutionary search operators are designed to exploit the structure of the grammar. The approach generates a set of symbolic models which collectively provide a tradeoff between error and model complexity. Experimental results show that the symbolic models generated are compact and easy to understand, making this an effective method for aiding understanding in analog design. The models also demonstrate better prediction quality than posynomials.
VizieR Online Data Catalog: Partition functions for molecules and atoms (Barklem+, 2016)
Barklem, P. S.; Collet, R.
2016-02-01
The results and input data are presented in the following files. Table 1 contains dissociation energies from the literature, and final adopted values, for 291 molecules. The literature values are from the compilations of Huber & Herzberg (1979, Constants of Diatomic Molecules (Van Nostrand Reinhold), Luo (2007, Comprehensive Handbook of Chemical Bond Energies (CRC Press)) and G2 theory calculations of Curtiss et al. (1991, J. Chem. Phys., 94, 7221). Table 2 contains the input data for the molecular calculations including adopted dissociation energy, nuclear spins, molecular spectroscopic constants and their sources. There are 291 files, one for each molecule, labelled by the molecule name. The various molecular spectroscopic constants are as defined in the paper. Table 4 contains the first, second and third ionisation energies for all chemical elements from H to U. The data comes from the CRC Handbook of Chemistry and Physics (Haynes, W.M. 2010, CRC Handbook of Chemistry and Physics, 91st edn. (CRC Press, Taylor and Francis Group)). Table 5a contains a list of keys to bibliographic references for the atomic energy level data that was extracted from NIST Atomic Spectra Database and used in the present work to compute atomic partition functions. The citation keys are abbreviations of the full bibliographic references which are made available in Table 5b in BibTeX format. Table 5b contains the full bibliographic references for the atomic energy level data that was extracted from the NIST Atomic Spectra Database. Table 6 contains tabulated partition function data as a function of temperature for 291 molecules. Table 7 contains tabulated equilibrium constant data as a function of temperature for 291 molecules. Table 8 contains tabulated partition function data as a function of temperature for 284 atoms and ions. The paper should be consulted for further details. (10 data files).
Semiclassical approximation to the partition function of a particle in D dimensions
Aragão de Carvalho, C; Fraga, E S; Jorás, S E
2000-01-01
We use a path integral formalism to derive the semiclassical series for the partition function of a particle in D dimensions. We analyze in particular the case of attractive central potentials, obtaining explicit expressions for the fluctuation determinant and for the semiclassical two-point function in the special cases of the harmonic and single-well quartic anharmonic oscillators. The specific heat of the latter is compared to precise WKB estimates. We conclude by discussing the possible extension of our results to field theories.
Semiclassical partition function for strings dual to Wilson loops with small cusps in ABJM
Aguilera-Damia, Jeremias; Silva, Guillermo A
2014-01-01
We compute the 1-loop partition function for strings in $AdS_4\\times\\mathbb{CP}^3$, whose worldsheets end along a line with small cusp angles in the boundary of AdS. We obtain these 1-loop results in terms of the vacuum energy for on-shell modes. Our results verify the proposal by Lewkowycz and Maldacena in arXiv:1312.5682 for the exact Bremsstrahlung function up to the next to leading order in the strong coupling expansion. The agreement is observed for cusps distorting either the 1/2 BPS or the 1/6 BPS Wilson line.
Semiclassical partition function for strings dual to Wilson loops with small cusps in ABJM
Aguilera-Damia, Jeremías; Correa, Diego H.; Silva, Guillermo A.
2015-03-01
We compute the 1-loop partition function for strings in , whose worldsheets end along a line with small cusp angles in the boundary of AdS. We obtain these 1-loop results in terms of the vacuum energy for on-shell modes. Our results verify the proposal by Lewkowycz and Maldacena in arXiv:1312.5682 for the exact Bremsstrahlung function up to the next to leading order in the strong coupling expansion. The agreement is observed for cusps distorting either the 1/2 BPS or the 1/6 BPS Wilson line.
Russo, Jorge G
2015-01-01
We exactly compute the partition function for $U(2)_k\\times U(2)_{-k}$ ABJM theory on $\\mathbb S^3$ deformed by mass $m$ and Fayet-Iliopoulos parameter $\\zeta $. For $k=1,2$, the partition function has an infinite number of Lee-Yang zeros. For general $k$, in the decompactification limit the theory exhibits a quantum (first-order) phase transition at $m=2\\zeta $.
Geometry of Spin and SPINc Structures in the M-Theory Partition Function
Sati, Hisham
We study the effects of having multiple Spin structures on the partition function of the spacetime fields in M-theory. This leads to a potential anomaly which appears in the eta invariants upon variation of the Spin structure. The main sources of such spaces are manifolds with nontrivial fundamental group, which are also important in realistic models. We extend the discussion to the Spinc case and find the phase of the partition function, and revisit the quantization condition for the C-field in this case. In type IIA string theory in 10 dimensions, the (mod 2) index of the Dirac operator is the obstruction to having a well-defined partition function. We geometrically characterize manifolds with and without such an anomaly and extend to the case of nontrivial fundamental group. The lift to KO-theory gives the α-invariant, which in general depends on the Spin structure. This reveals many interesting connections to positive scalar curvature manifolds and constructions related to the Gromov-Lawson-Rosenberg conjecture. In the 12-dimensional theory bounding M-theory, we study similar geometric questions, including choices of metrics and obtaining elements of K-theory in 10 dimensions by pushforward in K-theory on the disk fiber. We interpret the latter in terms of the families index theorem for Dirac operators on the M-theory circle and disk. This involves superconnections, eta forms, and infinite-dimensional bundles, and gives elements in Deligne cohomology in lower dimensions. We illustrate our discussion with many examples throughout.
Boundary superstring field theory annulus partition function in the presence of tachyons
International Nuclear Information System (INIS)
We compute the Boundary Superstring Field Theory partition function on the annulus in the presence of independent linear tachyon profiles on the two boundaries. The R-R sector is found to contribute non-trivially to the derivative terms of the space-time effective action. In the process we construct a boundary state description of D-branes in the presence of a linear tachyon. We quantize the open string in a tachyonic background and address the question of open/closed string duality. (author)
Potts Model Partition Functions for Self-Dual Families of Strip Graphs
Chang, Shu-Chiuan; Shrock, Robert
2001-01-01
We consider the $q$-state Potts model on families of self-dual strip graphs $G_D$ of the square lattice of width $L_y$ and arbitrarily great length $L_x$, with periodic longitudinal boundary conditions. The general partition function $Z$ and the T=0 antiferromagnetic special case $P$ (chromatic polynomial) have the respective forms $\\sum_{j=1}^{N_{F,L_y,\\lambda}} c_{F,L_y,j} (\\lambda_{F,L_y,j})^{L_x}$, with $F=Z,P$. For arbitrary $L_y$, we determine (i) the general coefficient $c_{F,L_y,j}$ i...
Chang, Shu-Chiuan; Shrock, Robert
2000-01-01
partial abstract: The $q$-state Potts model partition function (equivalent to the Tutte polynomial) for a lattice strip of fixed width $L_y$ and arbitrary length $L_x$ has the form $Z(G,q,v)=\\sum_{j=1}^{N_{Z,G,\\lambda}}c_{Z,G,j}(\\lambda_{Z,G,j})^{L_x}$, where $v$ is a temperature-dependent variable. The special case of the zero-temperature antiferromagnet ($v=-1$) is the chromatic polynomial $P(G,q)$. Using coloring and transfer matrix methods, we give general formulas for $C_{X,G}=\\sum_{j=1}...
Partition function of a chiral boson on a 2-torus from the Floreanini–Jackiw Lagrangian
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We revisit the problem of quantizing a chiral boson on a torus. The conventional approach is to extract the partition function of a chiral boson from the path integral of a non-chiral boson. Instead we compute it directly from the chiral boson Lagrangian of Floreanini and Jackiw modified by topological terms involving an auxiliary field. A careful analysis of the gauge-fixing condition for the extra gauge symmetry reproduces the correct results for the free chiral boson, and has the advantage of being applicable to a wider class of interacting chiral boson theories
International Nuclear Information System (INIS)
Multiple-diglycolamide-functionalized ligands (MDGA) in room temperature ionic liquids (RTILs) were studied for extraction of actinides and lanthanides from aqueous acidic solutions. The extraction kinetics, separation behavior, associated thermodynamics of extraction, nature of the extracted species formed were studied. Luminescence spectroscopy was used to understand the nature of bonding between metal and ligands, formation of inner sphere/outer sphere complex etc. The radiolytic stability of solvent systems was studied and attempt was made to understand the degradation products. Finally, all the systems were evaluated for 'actinide partitioning' from synthetic high level liquid waste solution (HLLW). (author)
Inner products of Bethe states as partial domain wall partition functions
Kostov, Ivan
2012-01-01
We study the inner product of Bethe states in the inhomogeneous periodic XXX spin-1/2 chain of length L, which is given by the Slavnov determinant formula. We show that the inner product of an on-shell M-magnon state with a generic M-magnon state is given by the same expression as the inner product of a 2M-magnon state with a vacuum descendent. The second inner product is proportional to the partition function of the six-vertex model on a rectangular Lx2M grid, with partial domain-wall boundary conditions.
Airy Equation for the Topological String Partition Function in a Scaling Limit
Alim, Murad; Yau, Shing-Tung; Zhou, Jie
2016-04-01
We use the polynomial formulation of the holomorphic anomaly equations governing perturbative topological string theory to derive the free energies in a scaling limit to all orders in perturbation theory for any Calabi-Yau threefold. The partition function in this limit satisfies an Airy differential equation in a rescaled topological string coupling. One of the two solutions of this equation gives the perturbative expansion and the other solution provides geometric hints of the non-perturbative structure of topological string theory. Both solutions can be expanded naturally around strong coupling.
Airy Equation for the Topological String Partition Function in a Scaling Limit
Alim, Murad; Yau, Shing-Tung; Zhou, Jie
2016-06-01
We use the polynomial formulation of the holomorphic anomaly equations governing perturbative topological string theory to derive the free energies in a scaling limit to all orders in perturbation theory for any Calabi-Yau threefold. The partition function in this limit satisfies an Airy differential equation in a rescaled topological string coupling. One of the two solutions of this equation gives the perturbative expansion and the other solution provides geometric hints of the non-perturbative structure of topological string theory. Both solutions can be expanded naturally around strong coupling.
Modular invariant partition functions for non-compact G/Ad(H) models
Bjornsson, Jonas
2010-01-01
We propose a spectrum for a class of gauged non-compact G/Ad(H) WZNW models, including spectrally flowed images of highest, lowest, and mixed extremal weight modules. These are combined into blocks whose characters, due to the Lorentzian signature of the target space, are divergent and treated as formal expressions in need of regularisation. Assuming that this is possible, we show that these extended characters transform linearly under modular transformations, and can be used to write down modular invariant partition functions.
Exact Partition Functions of Interacting Self-Avoiding Walks on Lattices
Hsieh, Yu-Hsin; Chen, Chi-Ning; Hu, Chin-Kun
2016-02-01
Ideas and methods of statistical physics have been shown to be useful for understanding some interesting problems in physical systems, e.g. universality and scaling in critical systems. The interacting self-avoiding walk (ISAW) on a lattice is the simplest model for homopolymers and serves as the framework of simple models for biopolymers, such as DNA, RNA, and protein, which are important components in complex systems in biology. In this paper, we briefly review our recent work on exact partition functions of ISAW. Based on zeros of these exact partition functions, we have developed a novel method in which both loci of zeros and thermodynamic functions associated with them are considered. With this method, the first zeros can be identified clearly without ambiguity. The critical point of a small system can then be defined as the peak position of the heat capacity component associated with the first zeros. For the system with two phase transitions, two pairs of first zeros corresponding to two phase transitions can be identified and overlapping Cυ can be well separated. ISAW on the simple cubic lattice is such a system where in addition to a standard collapse transition, there is another freezing transition occurring at a lower temperature. Our approach can give a clear scenario for the collapse and the freezing transitions.
Exact Partition Functions of Interacting Self-Avoiding Walks on Lattices
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Hsieh Yu-Hsin
2016-01-01
Full Text Available Ideas and methods of statistical physics have been shown to be useful for understanding some interesting problems in physical systems, e.g. universality and scaling in critical systems. The interacting self-avoiding walk (ISAW on a lattice is the simplest model for homopolymers and serves as the framework of simple models for biopolymers, such as DNA, RNA, and protein, which are important components in complex systems in biology. In this paper, we briefly review our recent work on exact partition functions of ISAW. Based on zeros of these exact partition functions, we have developed a novel method in which both loci of zeros and thermodynamic functions associated with them are considered. With this method, the first zeros can be identified clearly without ambiguity. The critical point of a small system can then be defined as the peak position of the heat capacity component associated with the first zeros. For the system with two phase transitions, two pairs of first zeros corresponding to two phase transitions can be identified and overlapping Cυ can be well separated. ISAW on the simple cubic lattice is such a system where in addition to a standard collapse transition, there is another freezing transition occurring at a lower temperature. Our approach can give a clear scenario for the collapse and the freezing transitions.
Buchanan, Paul J.; McCloskey, Karen D.
2016-01-01
The importance of ion channels in the hallmarks of many cancers is increasingly recognised. This article reviews current knowledge of the expression of members of the voltage-gated calcium channel family (CaV) in cancer at the gene and protein level and discusses their potential functional roles. The ten members of the CaV channel family are classified according to expression of their pore-forming α-subunit; moreover, co-expression of accessory α2δ, β and γ confers a spectrum of biophysical c...
Energy Technology Data Exchange (ETDEWEB)
Akemann, G. [Department of Mathematical Sciences and BURSt Research Centre, School of Information Systems, Computing and Mathematics, Brunel University West London, Uxbridge UB8 3PH (United Kingdom)]. E-mail: gernot.akemann@brunel.ac.uk; Basile, F. [Department of Mathematical Sciences and BURSt Research Centre, School of Information Systems, Computing and Mathematics, Brunel University West London, Uxbridge UB8 3PH (United Kingdom); Dipartimento di Fisica dell' Universita di Pisa and INFN, Via Buonarroti, 56127 Pisa (Italy)
2007-03-26
We compute all massive partition functions or characteristic polynomials and their complex eigenvalue correlation functions for non-Hermitean extensions of the symplectic and chiral symplectic ensemble of random matrices. Our results are valid for general weight functions without degeneracies of the mass parameters. The expressions we derive are given in terms of the Pfaffian of skew orthogonal polynomials in the complex plane and their kernel. They are much simpler than the corresponding expressions for symplectic matrix models with real eigenvalues, and we explicitly show how to recover these in the Hermitean limit. This explains the appearance of three different kernels as quaternion matrix elements there in terms of derivatives of a single kernel here.
Barklem, P. S.; Collet, R.
2016-04-01
Partition functions and dissociation equilibrium constants are presented for 291 diatomic molecules for temperatures in the range from near absolute zero to 10 000 K, thus providing data for many diatomic molecules of astrophysical interest at low temperature. The calculations are based on molecular spectroscopic data from the book of Huber & Herzberg (1979, Constants of Diatomic Molecules) with significant improvements from the literature, especially updated data for ground states of many of the most important molecules by Irikura (2007, J. Phys. Chem. Ref. Data, 36, 389). Dissociation energies are collated from compilations of experimental and theoretical values. Partition functions for 284 species of atoms for all elements from H to U are also presented based on data collected at NIST. The calculated data are expected to be useful for modelling a range of low density astrophysical environments, especially star-forming regions, protoplanetary disks, the interstellar medium, and planetary and cool stellar atmospheres. The input data, which will be made available electronically, also provides a possible foundation for future improvement by the community. Full Tables 1-8 are only available at the CDS via anonymous ftp to http://cdsarc.u-strasbg.fr (ftp://130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/588/A96
Grand canonical ensemble, multi-particle wave functions and scattering data
Bruckmann, Falk; Kloiber, Thomas; Sulejmanpasic, Tin
2015-01-01
We show that information about scattering data of a quantum field theory can be obtained from studying the system at finite density and low temperatures. In particular we consider models formulated on the lattice which can be exactly dualized to theories of conserved charge fluxes on lattice links. Apart from eliminating the complex action problem at nonzero chemical potential mu, these dualizations allow for a particle world line interpretation of the dual fluxes from which one can extract data about the 2-particle wave function. As an example we perform dual Monte Carlo simulations of the 2-dimensional O(3) model at nonzero mu and finite volume, whose non-perturbative spectrum consists of a massive triplet of particles. At nonzero mu particles are induced in the system, which at sufficiently low temperature give rise to sectors of fixed particle number. We show that the scattering phase shifts can be obtained either from the critical chemical potential values separating the sectors or directly from the wave...
Feldman, Michal; Tennenholtz, Moshe
We introduce partition equilibrium and study its existence in resource selection games (RSG). In partition equilibrium the agents are partitioned into coalitions, and only deviations by the prescribed coalitions are considered. This is in difference to the classical concept of strong equilibrium according to which any subset of the agents may deviate. In resource selection games, each agent selects a resource from a set of resources, and its payoff is an increasing (or non-decreasing) function of the number of agents selecting its resource. While it has been shown that strong equilibrium exists in resource selection games, these games do not possess super-strong equilibrium, in which a fruitful deviation benefits at least one deviator without hurting any other deviator, even in the case of two identical resources with increasing cost functions. Similarly, strong equilibrium does not exist for that restricted two identical resources setting when the game is played repeatedly. We prove that for any given partition there exists a super-strong equilibrium for resource selection games of identical resources with increasing cost functions; we also show similar existence results for a variety of other classes of resource selection games. For the case of repeated games we identify partitions that guarantee the existence of strong equilibrium. Together, our work introduces a natural concept, which turns out to lead to positive and applicable results in one of the basic domains studied in the literature.
The partition function of interfaces from the Nambu-Goto effective string theory
Billo, M; Ferro, L
2006-01-01
We consider the Nambu-Goto bosonic string model as a description of the physics of interfaces. By using the standard covariant quantization of the bosonic string, we derive an exact expression for the partition function in dependence of the geometry of the interface. Our expression, obtained by operatorial methods, resums the loop expansion of the NG model in the "physical gauge" computed perturbatively by functional integral methods in the literature. Recently, very accurate Monte Carlo data for the interface free energy in the 3d Ising model became avaliable. Our proposed expression compares very well to the data for values of the area sufficiently large in terms of the inverse string tension. This pattern is expected on theoretical grounds and agrees with previous analyses of other observables in the Ising model.
Xie, Wen-Jie; Jiang, Zhi-Qiang; Gu, Gao-Feng; Xiong, Xiong; Zhou, Wei-Xing
2015-10-01
Many complex systems generate multifractal time series which are long-range cross-correlated. Numerous methods have been proposed to characterize the multifractal nature of these long-range cross correlations. However, several important issues about these methods are not well understood and most methods consider only one moment order. We study the joint multifractal analysis based on partition function with two moment orders, which was initially invented to investigate fluid fields, and derive analytically several important properties. We apply the method numerically to binomial measures with multifractal cross correlations and bivariate fractional Brownian motions without multifractal cross correlations. For binomial multifractal measures, the explicit expressions of mass function, singularity strength and multifractal spectrum of the cross correlations are derived, which agree excellently with the numerical results. We also apply the method to stock market indexes and unveil intriguing multifractality in the cross correlations of index volatilities.
Energy Technology Data Exchange (ETDEWEB)
Wu, M.-C.; Hu, C.-K. [Institute of Physics, Academia Sinica, Nankang, Taipei, Taiwan (China)]. E-mails: mcwu@phys.sinica.edu.tw; huck@phys.sinica.edu.tw
2002-06-28
The Grassmann path integral approach is used to calculate exact partition functions of the Ising model on MxN square (sq), plane triangular (pt) and honeycomb (hc) lattices with periodic-periodic (pp), periodic-antiperiodic (pa), antiperiodic-periodic (ap) and antiperiodic-antiperiodic (aa) boundary conditions. The partition functions are used to calculate and plot the specific heat, C/k{sub B}, as a function of temperature, {theta}=k{sub B}T/J. We find that for the NxN sq lattice, C/k{sub B} for pa and ap boundary conditions are different from those for aa boundary conditions, but for the N x N pt and hc lattices, C/k{sub B} for ap, pa and aa boundary conditions have the same values. Our exact partition functions might also be useful for understanding the effects of lattice structures and boundary conditions on critical finite-size corrections of the Ising model. (author)
Partition function expansion on region graphs and message-passing equations
International Nuclear Information System (INIS)
Disordered and frustrated graphical systems are ubiquitous in physics, biology, and information science. For models on complete graphs or random graphs, deep understanding has been achieved through the mean-field replica and cavity methods. But finite-dimensional 'real' systems remain very challenging because of the abundance of short loops and strong local correlations. A statistical mechanics theory is constructed in this paper for finite-dimensional models based on the mathematical framework of the partition function expansion and the concept of region graphs. Rigorous expressions for the free energy and grand free energy are derived. Message-passing equations on the region graph, such as belief propagation and survey propagation, are also derived rigorously. (letter)
Twists of Plücker Coordinates as Dimer Partition Functions
Marsh, R. J.; Scott, J. S.
2016-02-01
The homogeneous coordinate ring of the Grassmannian Gr k, n has a cluster structure defined in terms of planar diagrams known as Postnikov diagrams. The cluster corresponding to such a diagram consists entirely of Plücker coordinates. We introduce a twist map on Gr k, n , related to the Berenstein-Fomin-Zelevinsky-twist, and give an explicit Laurent expansion for the twist of an arbitrary Plücker coordinate in terms of the cluster variables associated with a fixed Postnikov diagram. The expansion arises as a (scaled) dimer partition function of a weighted version of the bipartite graph dual to the Postnikov diagram, modified by a boundary condition determined by the Plücker coordinate. We also relate the twist map to a maximal green sequence.
Stochastic processes with ZN symmetry and complex Virasoro representations. The partition functions
International Nuclear Information System (INIS)
In a previous letter (Alcaraz F C et al 2014 J. Phys. A: Math. Theor. 47 212003) we have presented numerical evidence that a Hamiltonian expressed in terms of the generators of the periodic Temperley–Lieb algebra has, in the finite-size scaling limit, a spectrum given by representations of the Virasoro algebra with complex highest weights. This Hamiltonian defines a stochastic process with a ZN symmetry. We give here analytical expressions for the partition functions for this system which confirm the numerics. For N even, the Hamiltonian has a symmetry which makes the spectrum doubly degenerate leading to two independent stochastic processes. The existence of a complex spectrum leads to an oscillating approach to the stationary state. This phenomenon is illustrated by an example. (fast track communication)
Modular invariant partition functions for the doubly extended N=4 superconformal algebras
Energy Technology Data Exchange (ETDEWEB)
Ooguri, Hirosi (Research Inst. for Mathematical Sciences, Kyoto Univ. (Japan) Enrico Fermi Inst., Univ. of Chicago, IL (United States)); Petersen, J.L. (Niels Bohr Inst., Copenhagen (Denmark)); Taormina, A. (Enrico Fermi Inst., Univ. of Chicago, IL (United States))
1992-01-20
Non-trivial modular properties of characters of the doubly extended N=4 superconformal algebras A{sub {gamma}}, A{sub {gamma}} are derived from two different points of view. First, we use realizations on Wolf spaces, in particular when one of the levels of the two commuting affine SU(2) subalgebras takes the value 2. We emphasize how these realizations involve rational torus theories, and how some specific combinations of massless characters transform under the modular group as affine SU(2) characters. Second, we show how these combinations, and generalizations thereof, emerge from a study of the explicit form of the characters when angular variables are partly restricted, but the levels are not. The two results are then combined to give stringent constraints on the modular invariant A{sub {gamma}} partition functions and they give rise to a partial classification of the latter, closely related to that of affine SU(2). (orig.).
Modular invariant partition functions for the doubly extended N = 4 superconformal algebras
Ooguri, Hirosi; Petersen, Jens Lyng; Taormina, Anne
1992-01-01
Non-trivial modular properties of characters of the doubly extended N = 4 superconformal algebras Aγ, Ãγ are derived from two different points of view. First, we use realizations on Wolf spaces, in particular when one of the levels of the two commuting affine SU(2) subalgebras takes the value 2. We emphasize how these realizations involve rational torus theories, and how some specific combinations of massless characters transform under the modular group as affine SU(2) characters. Second, we show how these combinations, and generalizations thereof, emerge from a study of the explicit form of the characters when angular variables are partly restricted, but the levels are not. The two results are then combined to give stringent constraints on the modular invariant Ãγ partition functions and they give rise to a partial classification of the latter, closely related to that of affine SU(2).
Singularities of the Partition Function for the Ising Model Coupled to 2D Quantum Gravity
Ambjørn, J.; Anagnostopoulos, K. N.; Magnea, U.
We study the zeros in the complex plane of the partition function for the Ising model coupled to 2D quantum gravity for complex magnetic field and real temperature, and for complex temperature and real magnetic field, respectively. We compute the zeros by using the exact solution coming from a two-matrix model and by Monte-Carlo simulations of Ising spins on dynamical triangulations. We present evidence that the zeros form simple one-dimensional curves in the complex plane, and that the critical behaviour of the system is governed by the scaling of the distribution of the singularities near the critical point. Despite the small size of the systems studied, we can obtain a reasonable estimate of the (known) critical exponents.
Restricted Partition Functions and Inverse Energy Cascades in Parity Symmetry Breaking flows
Herbert, Corentin
2014-01-01
When the symmetries of homogenous isotropic turbulent flows are broken, different sets of modes with different physical roles emerge. In particular, choosing a forcing which puts more weight on one or the other of these sets may result in different statistics for the energy transfers. We use the general method of computing a partition function restricted to a portion of phase space to study analytically these different statistics. We illustrate this method in the case of parity symmetry breaking, measured by helicity. It is shown that when helicity is sign definite at all scales, an inverse cascade is expected for the energy. When sign-definiteness is lost, even for a small set of modes, this cascade disappears and there is a sharp phase transition to the standard helical equipartition spectra.
Two-loop partition function in the planar plane-wave matrix model
Spradlin, Marcus; Van Raamsdonk, Mark; Volovich, Anastasia
2004-12-01
We perform two independent calculations of the two-loop partition function for the 't Hooft large N limit of the plane-wave matrix model, conjectured to be dual to the decoupled little string theory of a single spherical type IIA NS5-brane. The first is via a direct two-loop path-integral calculation in the matrix model, while the second employs the one-loop dilatation operator of four-dimensional N = 4 Yang-Mills theory truncated to the SU (2 | 4) subsector. We find precise agreement between the results of the two calculations. Various polynomials appearing in the result have rather special properties, possibly related to the large symmetry algebra of the theory or to integrability.
Two-Loop Partition Function in the Planar Plane-Wave Matrix Model
Spradlin, M; Volovich, A; Spradlin, Marcus; Raamsdonk, Mark Van; Volovich, Anastasia
2004-01-01
We perform two independent calculations of the two-loop partition function for the large N 't Hooft limit of the plane-wave matrix model, conjectured to be dual to the decoupled little string theory of a single spherical type IIA NS5-brane. The first is via a direct two-loop path-integral calculation in the matrix model, while the second employs the one-loop dilatation operator of four-dimensional N = 4 Yang-Mills theory truncated to the SU(2|4) subsector. We find precise agreement between the results of the two calculations. Various polynomials appearing in the result have rather special properties, possibly related to the large symmetry algebra of the theory or to integrability.
International Nuclear Information System (INIS)
A detailed study of the S-K model through the analysis of the zeros of the partition function in the complex temperature plane is performed. By the exact way, the notable thermodynamical properties of the system to a variety of the length (N=5→25 spins) are calculated, using only standards concepts (without the use of tricks like that of replicas). Dilute models had been also considered. The principal result of this work is the characterization of the zeros of the partition function of the S-K model. (author)
Thermodynamic signatures of an underlying quantum phase transition: A grand canonical approach
Jimenez, Kevin; Reslen, Jose
2016-08-01
The grand canonical formalism is employed to study the thermodynamic structure of a model displaying a quantum phase transition when studied with respect to the canonical formalism. A numerical survey shows that the grand partition function diverges following a power law when the interaction parameter approaches a limiting constant. The power-law exponent takes a distinctive value when such limiting constant coincides with the critical point of the subjacent quantum phase transition. An approximated expression for the grand partition function is derived analytically implementing a mean field scheme and a number of thermodynamic observables are obtained. The system observables show signatures that can be used to track the critical point of the underlying transition. This result provides a simple fact that can be exploited to verify the existence of a quantum phase transition avoiding the zero temperature regime.
Canonical Quantum Statistics of Schwarzschild Black Holes and Ising Droplet Nucleation
Kastrup, H. A.
1997-01-01
Recently is was shown that the imaginary part of the canonical partition function of Schwarzschild black holes with an energy spectrum E_n = \\sigma \\sqrt{n} E_P, n= 1,2, ..., has properties which - naively interpreted - leads to the expected unusual thermodynamical properties of such black holes (Hawking temperature, Bekenstein-Hawking entropy etc). The present paper interprets the same imaginary part in the framework of droplet nucleation theory in which the rate of transition from a metasta...
Partition function, metastability, and kinetics of the escape transition for an ideal chain
Klushin, L. I.; Skvortsov, A. M.; Leermakers, F. A.
2004-06-01
An end-tethered polymer chain squeezed between two pistons undergoes an abrupt transition from a confined coil state to an inhomogeneous flower-like conformation partially escaped from the gap. We present a rigorous analytical theory for the equilibrium and kinetic aspects of this phenomenon for a Gaussian chain. Applying the analogy with the problem of the adsorption of an ideal chain constrained by one of its ends, we obtain a closed analytical expression for the exact partition function. Various equilibrium thermodynamic characteristics (the fraction of imprisoned segments, the average compression, and lateral forces) are calculated as a function of the piston separation. The force versus separation curve is studied in two complementary statistical ensembles, the constant force and the constant confinement width ones. The differences in these force curves are significant in the transition region for large systems, but disappear for small systems. The effects of metastability are analyzed by introducing the Landau free energy as a function of the chain stretching, which serves as the order parameter. The phase diagram showing the binodal and two spinodal lines is presented. We obtain the barrier heights between the stable and metastable states in the free energy landscape. The mean first passage time, i.e., the lifetime of the metastable coil and flower states, is estimated on the basis of the Fokker-Planck formalism. Equilibrium analytical theory for a Gaussian chain is complemented by numerical calculations for a lattice freely jointed chain model.
Directory of Open Access Journals (Sweden)
Jonathan Witztum
Full Text Available The availability of many complete, annotated proteomes enables the systematic study of the relationships between protein conservation and functionality. We explore this question based solely on the presence or absence of protein homologues (a.k.a. conservation profiles. We study 18 metazoans, from two distinct points of view: the human's and the fly's. Using the GOrilla gene ontology (GO analysis tool, we explore functional enrichment of the "universal proteins", those with homologues in all 17 other species, and of the "non-universal proteins". A large number of GO terms are strongly enriched in both human and fly universal proteins. Most of these functions are known to be essential. A smaller number of GO terms, exhibiting markedly different properties, are enriched in both human and fly non-universal proteins. We further explore the non-universal proteins, whose conservation profiles are consistent with the "tree of life" (TOL consistent, as well as the TOL inconsistent proteins. Finally, we applied Quantum Clustering to the conservation profiles of the TOL consistent proteins. Each cluster is strongly associated with one or a small number of specific monophyletic clades in the tree of life. The proteins in many of these clusters exhibit strong functional enrichment associated with the "life style" of the related clades. Most previous approaches for studying function and conservation are "bottom up", studying protein families one by one, and separately assessing the conservation of each. By way of contrast, our approach is "top down". We globally partition the set of all proteins hierarchically, as described above, and then identify protein families enriched within different subdivisions. While supporting previous findings, our approach also provides a tool for discovering novel relations between protein conservation profiles, functionality, and evolutionary history as represented by the tree of life.
Witztum, Jonathan; Persi, Erez; Horn, David; Pasmanik-Chor, Metsada; Chor, Benny
2014-01-01
The availability of many complete, annotated proteomes enables the systematic study of the relationships between protein conservation and functionality. We explore this question based solely on the presence or absence of protein homologues (a.k.a. conservation profiles). We study 18 metazoans, from two distinct points of view: the human's and the fly's. Using the GOrilla gene ontology (GO) analysis tool, we explore functional enrichment of the "universal proteins", those with homologues in all 17 other species, and of the "non-universal proteins". A large number of GO terms are strongly enriched in both human and fly universal proteins. Most of these functions are known to be essential. A smaller number of GO terms, exhibiting markedly different properties, are enriched in both human and fly non-universal proteins. We further explore the non-universal proteins, whose conservation profiles are consistent with the "tree of life" (TOL consistent), as well as the TOL inconsistent proteins. Finally, we applied Quantum Clustering to the conservation profiles of the TOL consistent proteins. Each cluster is strongly associated with one or a small number of specific monophyletic clades in the tree of life. The proteins in many of these clusters exhibit strong functional enrichment associated with the "life style" of the related clades. Most previous approaches for studying function and conservation are "bottom up", studying protein families one by one, and separately assessing the conservation of each. By way of contrast, our approach is "top down". We globally partition the set of all proteins hierarchically, as described above, and then identify protein families enriched within different subdivisions. While supporting previous findings, our approach also provides a tool for discovering novel relations between protein conservation profiles, functionality, and evolutionary history as represented by the tree of life. PMID:24594619
Pattern-Driven Architectural Partitioning. Balancing Functional and Non-functional Requirements
Harrison, Neil; Avgeriou, Paris
2007-01-01
One of the vexing challenges of software architecture is the problem of satisfying the functional specifications of the system to be created while at the same time meeting its non-functional needs. In this work we focus on the early stages of the software architecture process, when initial high-leve
Partition function on spheres: how (not) to use zeta function regularization
Monin, A
2016-01-01
It is known that not all summation methods are linear and stable. Zeta function regularization is in general non-linear. However, in some cases formal manipulations with "zeta function" regularization (assuming linearity of sums) lead to correct results. We consider several examples and show why this happens.
Zhang, Zhen; Lim, Chae Young; Maiti, Tapabrata; Kato, Seiji
2016-01-01
In climate change study, the infrared spectral signatures of climate change have recently been conceptually adopted, and widely applied to identifying and attributing atmospheric composition change. We propose a Bayesian hierarchical model for spatial clustering of the high-dimensional functional data based on the effects of functional covariates and local features. We couple the functional mixed-effects model with a generalized spatial partitioning method for: (1) producing spatially contigu...
Exact partition functions for the $\\Omega$-deformed $\\mathcal N=2^{*}$ $SU(2)$ gauge theory
Beccaria, Matteo
2016-01-01
We study the low energy effective action of the $\\Omega$-deformed $\\mathcal N =2^{*}$ $SU(2) $ gauge theory. It depends on the deformation parameters $\\epsilon_{1},\\epsilon_{2}$, the scalar field expectation value $a$, and the hypermultiplet mass $m$. We explore the plane $(\\frac{m}{\\epsilon_{1}}, \\frac{\\epsilon_{2}}{\\epsilon_{1}})$ looking for special features in the multi-instanton contributions to the prepotential, motivated by what happens in the Nekrasov-Shatashvili limit $\\epsilon_{2}\\to 0$. We propose a simple condition on the structure of poles of the $k$-instanton prepotential and show that it is admissible at a finite set of points in the above plane. At these special points, the prepotential has poles at fixed positions independent on the instanton number. Besides and remarkably, both the instanton partition function and the full prepotential, including the perturbative contribution, may be given in closed form as functions of the scalar expectation value $a$ and the modular parameter $q$ appearing...
Temperature-dependent nuclear partition functions and abundances in the stellar interior
Nabi, Jameel-Un; Nasser Tawfik, Abdel; Ezzelarab, Nada; Abas Khan, Ali
2016-05-01
We calculate the temperature-dependent nuclear partition functions (TDNPFs) and nuclear abundances for 728 nuclei, assuming nuclear statistical equilibrium (NSE). The theories of stellar evolution support NSE. Discrete nuclear energy levels have been calculated microscopically, using the pn-QRPA theory, up to an excitation energy of 10 MeV in the calculation of the TDNPFs. This feature of our paper distinguishes it from previous calculations. Experimental data is also incorporated wherever available to ensure the reliability of our results. Beyond 10 MeV, we employ a simple Fermi gas model and perform integration over the nuclear level densities to approximate the TDNPFs. We calculate nuclidic abundances, using the Saha equation, as a function of three parameters: stellar density, stellar temperature and the lepton-to-baryon content of stellar matter. All these physical parameters are considered to be extremely important in the stellar interior. The results obtained in this paper show that the equilibrium configuration of nuclei remains unaltered by increasing the stellar density (only the calculated nuclear abundances increase by roughly the same order of magnitude). Increasing the stellar temperature smoothes the equilibrium configuration showing peaks at the neutron-number magic nuclei.
Canonical phylogenetic ordination.
Giannini, Norberto P
2003-10-01
A phylogenetic comparative method is proposed for estimating historical effects on comparative data using the partitions that compose a cladogram, i.e., its monophyletic groups. Two basic matrices, Y and X, are defined in the context of an ordinary linear model. Y contains the comparative data measured over t taxa. X consists of an initial tree matrix that contains all the xj monophyletic groups (each coded separately as a binary indicator variable) of the phylogenetic tree available for those taxa. The method seeks to define the subset of groups, i.e., a reduced tree matrix, that best explains the patterns in Y. This definition is accomplished via regression or canonical ordination (depending on the dimensionality of Y) coupled with Monte Carlo permutations. It is argued here that unrestricted permutations (i.e., under an equiprobable model) are valid for testing this specific kind of groupwise hypothesis. Phylogeny is either partialled out or, more properly, incorporated into the analysis in the form of component variation. Direct extensions allow for testing ecomorphological data controlled by phylogeny in a variation partitioning approach. Currently available statistical techniques make this method applicable under most univariate/multivariate models and metrics; two-way phylogenetic effects can be estimated as well. The simplest case (univariate Y), tested with simulations, yielded acceptable type I error rates. Applications presented include examples from evolutionary ethology, ecology, and ecomorphology. Results showed that the new technique detected previously overlooked variation clearly associated with phylogeny and that many phylogenetic effects on comparative data may occur at particular groups rather than across the entire tree. PMID:14530135
Nimon, Kim; Henson, Robin K.; Gates, Michael S.
2010-01-01
In the face of multicollinearity, researchers face challenges interpreting canonical correlation analysis (CCA) results. Although standardized function and structure coefficients provide insight into the canonical variates produced, they fall short when researchers want to fully report canonical effects. This article revisits the interpretation of…
Singh, Gurpreet; Sharma, Rohit; Singh, Kuldip
2015-09-01
Thermodynamic properties (compressibility coefficient Z γ , specific heat at constant volume c v , adiabatic coefficient γ a , isentropic coefficient γ i s e n , and sound speed c s ) of non-local thermodynamic equilibrium hydrogen thermal plasma have been investigated for different values of pressure and non-equilibrium parameter θ (=Te/Th) in the electron temperature range from 6000 K to 60 000 K. In order to estimate the influence of pressure derivative of partition function on thermodynamic properties, two cases have been considered: (a) in which pressure derivative of partition function is taken into account in the expressions and (b) without pressure derivative of partition function in their expressions. Here, the case (b) represents expressions already available in literature. It has been observed that the temperature from which pressure derivative of partition function starts influencing a given thermodynamic property increases with increase of pressure and non-equilibrium parameter θ. Thermodynamic property in the case (a) is always greater than its value in the case (b) for compressibility coefficient and specific heat at constant volume, whereas for adiabatic coefficient, isentropic coefficient, and sound speed, its value in the case (a) is always less than its value in the case (b). For a given value of θ, the relationship of compressibility coefficient with degree of ionization depends upon pressure in the case (a), whereas it is independent of pressure in the case (b). Relative deviation between the two cases shows that the influence of pressure derivative of partition function is significantly large and increases with the augmentation of pressure and θ for compressibility coefficient, specific heat at constant volume, and adiabatic coefficient, whereas for isentropic coefficient and sound speed, it is marginal even at high values of pressure and non-equilibrium parameter θ.
Chang, Shu-Chiuan; Shrock, Robert
2001-07-01
The q-state Potts model partition function (equivalent to the Tutte polynomial) for a lattice strip of fixed width Ly and arbitrary length Lx has the form Z(G,q,v)=∑ j=1N Z,G,λ c Z,G,j(λ Z,G,j) L x, where v is a temperature-dependent variable. The special case of the zero-temperature antiferromagnet ( v=-1) is the chromatic polynomial P( G, q). Using coloring and transfer matrix methods, we give general formulas for C X,G=∑ j=1N X,G,λ c X,G,j for X= Z, P on cyclic and Möbius strip graphs of the square and triangular lattice. Combining these with a general expression for the (unique) coefficient cZ, G, j of degree d in q: c (d)=U 2d( q/2) , where Un( x) is the Chebyshev polynomial of the second kind, we determine the number of λZ, G, j's with coefficient c( d) in Z( G, q, v) for these cyclic strips of width Ly to be n Z(L y,d)=(2d+1)(L y+d+1) -1{2L y}/{L y-d } for 0⩽ d⩽ Ly and zero otherwise. For both cyclic and Möbius strips of these lattices, the total number of distinct eigenvalues λZ, G, j is calculated to be N Z,L y,λ = {2L y}/{L y}. Results are also presented for the analogous numbers nP( Ly, d) and NP, Ly, λ for P( G, q). We find that nP( Ly,0)= nP( Ly-1,1)= MLy-1 (Motzkin number), nZ( Ly,0)= CLy (the Catalan number), and give an exact expression for NP, Ly, λ. Our results for NZ, Ly, λ and NP, Ly, λ apply for both the cyclic and Möbius strips of both the square and triangular lattices; we also point out the interesting relations NZ, Ly, λ=2 NDA, tri, Ly and NP, Ly, λ=2 NDA, sq, Ly, where NDA, Λ, n denotes the number of directed lattice animals on the lattice Λ. We find the asymptotic growths NZ, Ly, λ∼ Ly-1/24 Ly and NP, Ly, λ∼ Ly-1/23 Ly as Ly→∞. Some general geometric identities for Potts model partition functions are also presented.
Roghanian, Ali; Sallenave, Jean-Michel
2008-03-01
Proteases and antiproteases have multiple important roles both in normal homeostasis and during inflammation. Antiprotease molecules may have developed in a parallel network, consisting of "alarm" and "systemic" inhibitors. Their primary function was thought until recently to mainly prevent the potential injurious effects of excess release of proteolytic enzymes, such as neutrophil elastase (NE), from inflammatory cells. However, recently, new potential roles have been ascribed to these antiproteases. We will review "canonical" and new "noncanonical" functions for these molecules, and more particularly, those pertaining to their role in innate and adaptive immunity (antibacterial activity and biasing of the adaptive immune response). PMID:18518838
International Nuclear Information System (INIS)
We compute two- and three-body cluster functions that describe contributions of composite entities, like hydrogen atoms, ions H−, H2+, and helium atoms, and also charge-charge and atom-charge interactions, to the equation of state of a hydrogen-helium mixture at low density. A cluster function has the structure of a truncated virial coefficient and behaves, at low temperatures, like a usual partition function for the composite entity. Our path integral Monte Carlo calculations use importance sampling to sample efficiently the cluster partition functions even at low temperatures where bound state contributions dominate. We also employ a new and efficient adaptive discretization scheme that allows one not only to eliminate Coulomb divergencies in discretized path integrals, but also to direct the computational effort where particles are close and thus strongly interacting. The numerical results for the two-body function agree with the analytically known quantum second virial coefficient. The three-body cluster functions are compared at low temperatures with familiar partition functions for composite entities
Turkheimer, Federico E; Leech, Robert; Expert, Paul; Lord, Louis-David; Vernon, Anthony C
2015-08-01
A variety of anatomical and physiological evidence suggests that the brain performs computations using motifs that are repeated across species, brain areas, and modalities. The computational architecture of cortex, for example, is very similar from one area to another and the types, arrangements, and connections of cortical neurons are highly stereotyped. This supports the idea that each cortical area conducts calculations using similarly structured neuronal modules: what we term canonical computational motifs. In addition, the remarkable self-similarity of the brain observables at the micro-, meso- and macro-scale further suggests that these motifs are repeated at increasing spatial and temporal scales supporting brain activity from primary motor and sensory processing to higher-level behaviour and cognition. Here, we briefly review the biological bases of canonical brain circuits and the role of inhibitory interneurons in these computational elements. We then elucidate how canonical computational motifs can be repeated across spatial and temporal scales to build a multiplexing information system able to encode and transmit information of increasing complexity. We point to the similarities between the patterns of activation observed in primary sensory cortices by use of electrophysiology and those observed in large scale networks measured with fMRI. We then employ the canonical model of brain function to unify seemingly disparate evidence on the pathophysiology of schizophrenia in a single explanatory framework. We hypothesise that such a framework may also be extended to cover multiple brain disorders which are grounded in dysfunction of GABA interneurons and/or these computational motifs. PMID:25956253
Molecular orbital estimation of reduced partition function ratios of small water clusters
International Nuclear Information System (INIS)
Structures of water clusters, (H2O)n, up to n=10 were optimized at the HF/6-31G(d) level of theory, and H/D and 16O/18O isotopic reduced partition function ratios (RPFRs) at the optimized structures were calculated. The H/D RPFR values were distinctly different between hydrogen-bonded hydrogen atoms and non-hydrogen-bonded hydrogen atoms, but were nearly independent of the cluster size for n equal to 3 or larger when only the lowest-energy conformers are taken into consideration. The 16O/18O RPFR values were also distinct between hydrogen-bonded oxygen atoms and non-hydrogen-bonded oxygen atoms, but little difference in RPFR value was observed between oxygen atoms with one hydrogen bond and those with two hydrogen bonds. The 16O/18O RPFR values were cluster size independent above n=6. The estimation of RPFRs of liquid water thus seemed possible by considering the lowest energy conformers of small water clusters (n=6-10). (author)
Canonical density matrix perturbation theory.
Niklasson, Anders M N; Cawkwell, M J; Rubensson, Emanuel H; Rudberg, Elias
2015-12-01
Density matrix perturbation theory [Niklasson and Challacombe, Phys. Rev. Lett. 92, 193001 (2004)] is generalized to canonical (NVT) free-energy ensembles in tight-binding, Hartree-Fock, or Kohn-Sham density-functional theory. The canonical density matrix perturbation theory can be used to calculate temperature-dependent response properties from the coupled perturbed self-consistent field equations as in density-functional perturbation theory. The method is well suited to take advantage of sparse matrix algebra to achieve linear scaling complexity in the computational cost as a function of system size for sufficiently large nonmetallic materials and metals at high temperatures. PMID:26764847
Abroi, Aare; Ilves, Ivar; Kivi, Sirje; Ustav, Mart
2004-01-01
Recent studies have suggested that the tethering of viral genomes to host cell chromosomes could provide one of the ways to achieve their nuclear retention and partitioning during extrachromosomal maintenance in dividing cells. The data we present here provide firm evidence that the partitioning of the bovine papillomavirus type 1 (BPV1) genome is dependent on the chromatin attachment process mediated by viral E2 protein and its multiple binding sites. On the other hand, the attachment of E2 ...
Kallen, Johan; Zabzine, Maxim
2012-01-01
Based on the construction by Hosomichi, Seong and Terashima we consider N=1 supersymmetric 5D Yang-Mills theory with matter on a five-sphere with radius r. This theory can be thought of as a deformation of the theory in flat space with deformation parameter r and this deformation preserves 8 supercharges. We calculate the full perturbative partition function as a function of r/g^2, where g is the Yang-Mills coupling, and the answer is given in terms of a matrix model. We perform the calculation using localization techniques. We also argue that in the large N-limit of this deformed 5D Yang-Mills theory this matrix model provides the leading contribution to the partition function and the rest is exponentially suppressed.
Mielke, Steven L; Truhlar, Donald G
2016-01-21
Using Feynman path integrals, a molecular partition function can be written as a double integral with the inner integral involving all closed paths centered at a given molecular configuration, and the outer integral involving all possible molecular configurations. In previous work employing Monte Carlo methods to evaluate such partition functions, we presented schemes for importance sampling and stratification in the molecular configurations that constitute the path centroids, but we relied on free-particle paths for sampling the path integrals. At low temperatures, the path sampling is expensive because the paths can travel far from the centroid configuration. We now present a scheme for importance sampling of whole Feynman paths based on harmonic information from an instantaneous normal mode calculation at the centroid configuration, which we refer to as harmonically guided whole-path importance sampling (WPIS). We obtain paths conforming to our chosen importance function by rejection sampling from a distribution of free-particle paths. Sample calculations on CH4 demonstrate that at a temperature of 200 K, about 99.9% of the free-particle paths can be rejected without integration, and at 300 K, about 98% can be rejected. We also show that it is typically possible to reduce the overhead associated with the WPIS scheme by sampling the paths using a significantly lower-order path discretization than that which is needed to converge the partition function. PMID:26801023
Mielke, Steven L.; Truhlar, Donald G.
2016-01-01
Using Feynman path integrals, a molecular partition function can be written as a double integral with the inner integral involving all closed paths centered at a given molecular configuration, and the outer integral involving all possible molecular configurations. In previous work employing Monte Carlo methods to evaluate such partition functions, we presented schemes for importance sampling and stratification in the molecular configurations that constitute the path centroids, but we relied on free-particle paths for sampling the path integrals. At low temperatures, the path sampling is expensive because the paths can travel far from the centroid configuration. We now present a scheme for importance sampling of whole Feynman paths based on harmonic information from an instantaneous normal mode calculation at the centroid configuration, which we refer to as harmonically guided whole-path importance sampling (WPIS). We obtain paths conforming to our chosen importance function by rejection sampling from a distribution of free-particle paths. Sample calculations on CH4 demonstrate that at a temperature of 200 K, about 99.9% of the free-particle paths can be rejected without integration, and at 300 K, about 98% can be rejected. We also show that it is typically possible to reduce the overhead associated with the WPIS scheme by sampling the paths using a significantly lower-order path discretization than that which is needed to converge the partition function.
Constrained Canonical Correlation.
DeSarbo, Wayne S.; And Others
1982-01-01
A variety of problems associated with the interpretation of traditional canonical correlation are discussed. A response surface approach is developed which allows for investigation of changes in the coefficients while maintaining an optimum canonical correlation value. Also, a discrete or constrained canonical correlation method is presented. (JKS)
International Nuclear Information System (INIS)
An algorithm to approximately calculate the partition function (and subsequently ensemble averages) and density of states of lattice spin systems through non-Monte-Carlo random sampling is developed. This algorithm (called the sampling-the-mean algorithm) can be applied to models where the up or down spins at lattice nodes interact to change the spin states of other lattice nodes, especially non-Ising-like models with long-range interactions such as the biological model considered here. Because it is based on the Central Limit Theorem of probability, the sampling-the-mean algorithm also gives estimates of the error in the partition function, ensemble averages, and density of states. Easily implemented parallelization strategies and error minimizing sampling strategies are discussed. The sampling-the-mean method works especially well for relatively small systems, systems with a density of energy states that contains sharp spikes or oscillations, or systems with little a priori knowledge of the density of states
Potts model partition functions for self-dual families of strip graphs
Chang, Shu-Chiuan; Shrock, Robert
2001-12-01
We consider the q-state Potts model on families of self-dual strip graphs GD of the square lattice of width Ly and arbitrarily great length Lx, with periodic longitudinal boundary conditions. The general partition function Z and the T=0 antiferromagnetic special case P (chromatic polynomial) have the respective forms ∑ j=1 NF, Ly, λcF, Ly, j( λF, Ly, j) Lx, with F= Z, P. For arbitrary Ly, we determine (i) the general coefficient cF, Ly, j in terms of Chebyshev polynomials, (ii) the number nF( Ly, d) of terms with each type of coefficient, and (iii) the total number of terms NF, Ly, λ. We point out interesting connections between the nZ( Ly, d) and Temperley-Lieb algebras, and between the NF, Ly, λ and enumerations of directed lattice animals. Exact calculations of P are presented for 2⩽ Ly⩽4. In the limit of infinite length, we calculate the ground state degeneracy per site (exponent of the ground state entropy), W( q). Generalizing q from Z+ to C, we determine the continuous locus B in the complex q plane where W( q) is singular. We find the interesting result that for all Ly values considered, the maximal point at which B crosses the real q-axis, denoted qc, is the same, and is equal to the value for the infinite square lattice, qc=3. This is the first family of strip graphs of which we are aware that exhibits this type of universality of qc.
Experimental Energy Levels and Partition Function of the 12C2 Molecule
Furtenbacher, Tibor; Szabó, István; Császár, Attila G.; Bernath, Peter F.; Yurchenko, Sergei N.; Tennyson, Jonathan
2016-06-01
The carbon dimer, the 12C2 molecule, is ubiquitous in astronomical environments. Experimental-quality rovibronic energy levels are reported for 12C2, based on rovibronic transitions measured for and among its singlet, triplet, and quintet electronic states, reported in 42 publications. The determination utilizes the Measured Active Rotational-Vibrational Energy Levels (MARVEL) technique. The 23,343 transitions measured experimentally and validated within this study determine 5699 rovibronic energy levels, 1325, 4309, and 65 levels for the singlet, triplet, and quintet states investigated, respectively. The MARVEL analysis provides rovibronic energies for six singlet, six triplet, and two quintet electronic states. For example, the lowest measurable energy level of the {{a}}{}3{{{\\Pi }}}{{u}} state, corresponding to the J = 2 total angular momentum quantum number and the F 1 spin-multiplet component, is 603.817(5) cm‑1. This well-determined energy difference should facilitate observations of singlet–triplet intercombination lines, which are thought to occur in the interstellar medium and comets. The large number of highly accurate and clearly labeled transitions that can be derived by combining MARVEL energy levels with computed temperature-dependent intensities should help a number of astrophysical observations as well as corresponding laboratory measurements. The experimental rovibronic energy levels, augmented, where needed, with ab initio variational ones based on empirically adjusted and spin–orbit coupled potential energy curves obtained using the Duo code, are used to obtain a highly accurate partition function, and related thermodynamic data, for 12C2 up to 4000 K.
Multiplicity fluctuations in heavy-ion collisions using canonical and grand-canonical ensemble
Energy Technology Data Exchange (ETDEWEB)
Garg, P. [Indian Institute of Technology Indore, Discipline of Physics, School of Basic Science, Simrol (India); Mishra, D.K.; Netrakanti, P.K.; Mohanty, A.K. [Bhabha Atomic Research Center, Nuclear Physics Division, Mumbai (India)
2016-02-15
We report the higher-order cumulants and their ratios for baryon, charge and strangeness multiplicity in canonical and grand-canonical ensembles in ideal thermal model including all the resonances. When the number of conserved quanta is small, an explicit treatment of these conserved charges is required, which leads to a canonical description of the system and the fluctuations are significantly different from the grand-canonical ensemble. Cumulant ratios of total-charge and net-charge multiplicity as a function of collision energies are also compared in grand-canonical ensemble. (orig.)
Multiplicity fluctuations in heavy ion collisions using canonical and grand canonical ensemble
Garg, P; Netrakanti, P K; Mohanty, A K
2015-01-01
We report the higher order cumulants and their ratios for baryon, charge and strangeness multiplicity in canonical and grand-canonical ensembles in ideal thermal model including all the resonances. When the number of conserved quanta is small, an explicit treatment of these conserved charges is required, which leads to a canonical description of the system and the fluctuations are significantly different from the grand canonical ensemble. Cumulant ratios of total charge and net-charge multiplicity as a function of collision energies are also compared in grand canonical ensemble.
Pedro Higuchi; Ana Carolina da Silva; Manoela Drews de Aguiar; Álvaro Luiz Mafra; Marcelo Negrini; Diego Fernando Zech
2014-01-01
http://dx.doi.org/10.5902/1980509814580The relationship vegetation-soil can contribute to understand the forest structure, supporting biodiversity conservation. Thus, the aim of the present study was to verify the existence of spatial partition of the tree species community in an Araucaria forest fragment in function of soil drainage. For this sake, an environmental characterization (soil drainage, physical and chemical soil properties, topography, compression of soil, depth of soil and canop...
Partition function zeros for the Ising model on complete graphs and on annealed scale-free networks
International Nuclear Information System (INIS)
We analyse the partition function of the Ising model on graphs of two different types: complete graphs, wherein all nodes are mutually linked and annealed scale-free networks for which the degree distribution decays as P(k) ∼ k −λ. We are interested in zeros of the partition function in the cases of complex temperature or complex external field (Fisher and Lee–Yang zeros respectively). For the model on an annealed scale-free network, we find an integral representation for the partition function which, in the case λ > 5, reproduces the zeros for the Ising model on a complete graph. For 3 < λ < 5 we derive the λ-dependent angle at which the Fisher zeros impact onto the real temperature axis. This, in turn, gives access to the λ-dependent universal values of the critical exponents and critical amplitudes ratios. Our analysis of the Lee–Yang zeros reveals a difference in their behaviour for the Ising model on a complete graph and on an annealed scale-free network when 3 < λ < 5. Whereas in the former case the zeros are purely imaginary, they have a non zero real part in latter case, so that the celebrated Lee–Yang circle theorem is violated. (paper)
Institute of Scientific and Technical Information of China (English)
Serena Morigi; Fiorella Sgallari
2009-01-01
This paper introduces the use of partition of unity method for the develop-ment of a high order finite volume discretization scheme on unstructured grids for solv-ing diffusion models based on partial differential equations. The unknown function and its gradient can be accurately reconstructed using high order optimal recovery based on radial basis functions. The methodology proposed is applied to the noise removal prob-lem in functional surfaces and images. Numerical results demonstrate the effectiveness of the new numerical approach and provide experimental order of convergence.
Canonical and grand canonical theory of spinodal instabilities
International Nuclear Information System (INIS)
In the context of the mean field approximation to the Landau-Ginzburg-Wilson functional integral, describing the equilibrium properties of a system with a conserved order parameter, the conditions for critical instabilities in the canonical ensemble are analysed. (A.C.A.S.)
International Nuclear Information System (INIS)
The partition function of a planar Ising model on a finite lattice with magnetic fields on the boundaries is represented through the anticommuting functional integral with Gaussian distribution. In particular, the previously unknown solution for the case of fields of opposite direction is obtained. It is shown also that the partition function of the model at the critical point in the continuous limit can be expressed through certain characters of highest-weight irreducible representations of Virasoro algebra. 15 refs
Odabasi, Mustafa; Cetin, Eylem; Sofuoglu, Aysun
Octanol-air partition coefficients ( KOA) for 14 polycyclic aromatic hydrocarbons (PAHs) were determined as a function of temperature using the gas chromatographic retention time method. log KOA values at 25° ranged over six orders of magnitude, between 6.34 (acenaphthylene) and 12.59 (dibenz[ a,h]anthracene). The determined KOA values were within factor of 0.7 (dibenz[ a,h]anthracene) to 15.1 (benz[ a]anthracene) of values calculated as the ratio of octanol-water partition coefficient to dimensionless Henry's law constant. Supercooled liquid vapor pressures ( PL) of 13 PAHs were also determined using the gas chromatographic retention time technique. Activity coefficients in octanol calculated using KOA and PL ranged between 3.2 and 6.2 indicating near-ideal solution behavior. Atmospheric concentrations measured in this study in Izmir, Turkey were used to investigate the partitioning of PAHs between particle and gas-phases. Experimental gas-particle partition coefficients ( Kp) were compared to the predictions of KOA absorption and KSA (soot-air partition coefficient) models. Octanol-based absorptive partitioning model predicted lower partition coefficients especially for relatively volatile PAHs. Ratios of measured/modeled partition coefficients ranged between 1.1 and 15.5 (4.5±6.0, average±SD) for KOA model. KSA model predictions were relatively better and measured to modeled ratios ranged between 0.6 and 5.6 (2.3±2.7, average±SD).
On partitions avoiding right crossings
Yan, Sherry H. F.; Xu, Yuexiao
2011-01-01
Recently, Chen et al. derived the generating function for partitions avoiding right nestings and posed the problem of finding the generating function for partitions avoiding right crossings. In this paper, we derive the generating function for partitions avoiding right crossings via an intermediate structure of partial matchings avoiding 2-right crossings and right nestings. We show that there is a bijection between partial matchings avoiding 2-right crossing and right nestings and partitions...
Properties of the linear canonical integral transformation.
Alieva, Tatiana; Bastiaans, Martin J
2007-11-01
We provide a general expression and different classification schemes for the general two-dimensional canonical integral transformations that describe the propagation of coherent light through lossless first-order optical systems. Main theorems for these transformations, such as shift, scaling, derivation, etc., together with the canonical integral transforms of selected functions, are derived. PMID:17975592
Zhou, C-J; Borello, U; Rubenstein, J L R; Pleasure, S J
2006-11-01
To better understand the function of the Wnt pathway in the developing telencephalon, we analyzed neocortical development in low density lipoprotein receptor-related protein (LRP) 6 mutants. LRP6 mutant mice are hypomorphic for the canonical Wnt signaling pathway and have hypoplasia of the developing neocortex. While early telencephalic morphogenesis is largely intact in these mice, probably due to compensation by LRP5, the mutant mice develop a dramatically thinner cortical plate. There is a prominent reduction of neurogenesis leading to a thin cortical plate. Reduced proliferation late in gestation probably also contributes to the hypoplasia. Although there are marked decreases in the numbers of layer 6 and layers 2-4 neurons all laminar identities are generated and there is no evidence of compensatory increases in layer 5 neurons. In addition, LRP6 mutants have partial penetrance of a complex of cortical dysmorphologies resembling those found in patients with developmental forms of epilepsy and mental retardation. These include ventricular and marginal zone heterotopias and cobblestone lissencephaly. This analysis demonstrates that canonical Wnt signaling is required for a diverse array of developmental processes in the neocortex in addition to the previously known roles in regulating precursor proliferation and patterning. PMID:16920270
Marine microalgae growth and carbon partitioning as a function of nutrient availability.
Fernandes, Tomásia; Fernandes, Igor; Andrade, Carlos A P; Cordeiro, Nereida
2016-08-01
To understand in which way the structural differences of three marine microalgae (Nannochloropsis gaditana, Rhodomonas marina and Isochrysis sp.) affect their carbon partitioning, growth and applicability; a stoichiometric imbalance was imposed by steady carbon and other nutrients variation. Towards high nutrients concentrations/low carbon availability a decrease of 12-51% in C/N microalgae ratio was observed and maximum cell densities were achieved. Moreover, linear correlation between the nutrient input and microalgae protein content were observed. The macromolecular ratios pointed that carbohydrate was the main contributor for the C/N decrement. Although lipid content in R. marina remained constant throughout the experiment, a rise of 37-107% in N. gaditana and Isochrysis sp. was verified. Lipid fractions revealed high percentages of glycolipids in all microalgae (57-73% of total lipids). The present study shows an easy way to understand and modulate microalgae carbon partitioning relying on the field of application. PMID:27179298
Rainforth, Tom; Wood, Frank
2015-01-01
We introduce canonical correlation forests (CCFs), a new decision tree ensemble method for classification. Individual canonical correlation trees are binary decision trees with hyperplane splits based on canonical correlation components. Unlike axis-aligned alternatives, the decision surfaces of CCFs are not restricted to the coordinate system of the input features and therefore more naturally represent data with correlation between the features. Additionally we introduce a novel alternative ...
Process modelling on a canonical basis[Process modelling; Canonical modelling
Energy Technology Data Exchange (ETDEWEB)
Siepmann, Volker
2006-12-20
possible to retrieve symbolically obtained derivatives of arbitrary process properties with respect to process parameters efficiently as a post calculation. The approach is therefore perfectly suitable to perform advanced process systems engineering tasks, such as sensitivity analysis, process optimisation, and data reconciliation. The concept of canonical modelling yields a natural definition of a general exergy state function for second law analysis. By partitioning of exergy into latent, mechanical, and chemical contributions, irreversible effects can be identified specifically, even for black-box models. The calculation core of a new process simulator called Yasim is developed and implemented. The software design follows the concepts described in the theoretical part of this thesis. Numerous exemplary process models are presented to address various subtopics of canonical modelling (author)
International Nuclear Information System (INIS)
Based on the ab initio molecular orbital theory at the HF/6-31G(d) level, the effect of hydration on the reduced partition function ratio(RPFR) of the monoborate anion (B(OH)4-) is evaluated in order to better understand boron isotope fractionation observed in aqueous systems. Aquoborate anions up to decaaquoborate anion, B(OH)4-(H2O)10, were considered and their geometry optimization and RPFR calculations were carried out. It was induced that hydration decreased the ln(RPFR) value of B(OH)4- by ca. 1.2%. (author)
Chang, Shu-Chiuan; Shrock, Robert
2015-11-01
We calculate the partition function of the q-state Potts model on arbitrary-length cyclic ladder graphs of the square and triangular lattices, with a generalized external magnetic field that favors or disfavors a subset of spin values {1,ldots ,s} with s ≤ q. For the case of antiferromagnet spin-spin coupling, these provide exactly solved models that exhibit an onset of frustration and competing interactions in the context of a novel type of tensor-product S_s ⊗ S_{q-s} global symmetry, where S_s is the permutation group on s objects.
Partition function, metastability, and kinetics of the escape transition for an ideal chain
Klushin, L.I.; Skvortsov, A.M.; Leermakers, F.A.M.
2004-01-01
The exact partition of the gaussian chain squeezed between two cylinders for a phase transition in a single macromolecule is analyzed. The polymer chain is squeezed between two pistons which results in abrupt transition from a confined coil state to an inhomogeneous conformation. The landau free energy is used in a one dimensional fokker-plank equation to predict the life-time of the metastable states. The analysis shows that the mean first passage time is estimated on the basis of the fokker...
Dunkl Operators and Canonical Invariants of Reflection Groups
Arkady Berenstein; Yurii Burman
2008-01-01
Using Dunkl operators, we introduce a continuous family of canonical invariants of finite reflection groups. We verify that the elementary canonical invariants of the symmetric group are deformations of the elementary symmetric polynomials. We also compute the canonical invariants for all dihedral groups as certain hypergeometric functions.
Guo, J.; Hungate, B. A.; Kolb, T.; KOCH, G. W.
2012-12-01
In semi-arid environments, co-existing plant species may vary in rooting depth, reflecting functional differences in water sources. In mountains of the southwestern U.S., moisture availability increases with elevation and winter and summer precipitation inputs differ isotopically. Examining variation in functional rooting depth among different plant communities and seasons is important to understanding how these communities may respond to the predicted warming and drying of the Southwest. The goal of this study was to assess the water partitioning of the woody plant community along an elevational moisture gradient using water isotopes as a proxy for rooting depth. We hypothesized that spatial and temporal water partitioning would be greatest in low elevation, moisture-stressed sites and would decrease as moisture availability increases with elevation. Five plots were established in each of five biotic communities: upland Sonoran desert, pinyon-juniper woodland, ponderosa pine forest, mixed-conifer forest, and spruce-fir forest. Soils (surface, 20 cm, 40 cm) and stem samples of dominant woody perennials were sampled during the late spring dry season and in late summer following monsoon rains, water was extracted using a cryo-vacuum line, and δD and δ18O values were determined by off-axis cavity ringdown spectroscopy. Soil moisture content increased with elevation across all sites and increased with soil depth in the desert, pinyon-juniper, and ponderosa sites. The δD values differed significantly among species in the desert and the ponderosa forest communities (p=0.014 and 0.039 ), while no species differences in δD were found in the pinyon-juniper woodland or mixed-conifer forest. With the exception of the pinyon-juniper woodland, these data support our hypothesis that niche differentiation between species becomes less significant higher on the topographic moisture gradient, in the mixed-conifer forest. While spatial water partitioning mostly follows our
Directory of Open Access Journals (Sweden)
Carlos García-Bedoya Maguiña
2011-05-01
Full Text Available Canon es un concepto clave en la historia literaria. En el presente artículo,se revisa la evolución histórica del canon literario peruano. Es solo con la llamada República Aristocrática, en las primeras décadas del siglo XX, que cabe hablar en el caso peruano de la formación de un auténtico canon nacional. El autor denomina a esta primera versión del canon literario peruano como canon oligárquico y destaca la importancia de la obra de Riva Agüero y de Ventura García Calderón en su configuración. Es solo más tarde, desde los años 20 y de modo definitivo desde los años 50, que puede hablarse de la emergencia de un nuevo canon literarioal que el autor propone determinar canon posoligárquico.
Directory of Open Access Journals (Sweden)
Jia Hu
Full Text Available The Tibetan Plateau (TP is predicted to experience increases in air temperature, increases in snowfall, and decreases in monsoon rains; however, there is currently a paucity of data that examine the ecological responses to such climate changes. In this study, we examined the effects of increased air temperature and snowfall on: 1 water use partitioning by different plant functional groups, and 2 ecosystem CO2 fluxes throughout the growing season. At the individual plant scale, we used stable hydrogen isotopes (δD to partition water use between shallow- and deep-rooted species. Prior to the arrival of summer precipitation (typically mid-July, snowmelt was the main water source in the soils. During this time, shallow and deep-rooted species partitioned water use by accessing water from shallow and deep soils, respectively. However, once the monsoon rains arrived, all plants used rainwater from the upper soils as the main water source. Snow addition did not result in increased snowmelt use throughout the growing season; instead, snowmelt water was pushed down into deeper soils when the rains arrived. At the larger plot scale, CO2 flux measurements demonstrated that rain was the main driver for net ecosystem productivity (NEP. NEP rates were low during June and July and reached a maximum during the monsoon season in August. Warming decreased NEP through a reduction in gross primary productivity (GPP, and snow additions did not mitigate the negative effects of warming by increasing NEP or GPP. Both the isotope and CO2 flux results suggest that rain drives productivity in the Nam Tso region on the TP. This also suggests that the effects of warming-induced drought on the TP may not be mitigated by increased snowfall. Further decreases in summer monsoon rains may affect ecosystem productivity, with large implications for livestock-based livelihoods.
Oka, Shotaro
2015-01-01
The canonical approach for finite density lattice QCD has a numerical instability. This instability makes it difficult to use the method reliably at the finite real chemical potential region. We studied this instability in detail and found that it is caused by the cancellation of significant digits. In order to reduce the effect of this cancellation, we adopt the multiple precision calculation for our discrete Fourier transformation (DFT) program, and we get the canonical partition function Zc(n,T) with required accuracy. From the obtained Zc(n,T), we calculate Lee--Yang zero distribution varying the number of significant digits. As a result, some curves surround the origin in the fugacity plane, but they are moved by varying the number of significant digits. Hence, we conclude that these curves are pseudo phase transition lines, and not real ones.
Directory of Open Access Journals (Sweden)
Pedro Higuchi
2014-06-01
Full Text Available http://dx.doi.org/10.5902/1980509814580The relationship vegetation-soil can contribute to understand the forest structure, supporting biodiversity conservation. Thus, the aim of the present study was to verify the existence of spatial partition of the tree species community in an Araucaria forest fragment in function of soil drainage. For this sake, an environmental characterization (soil drainage, physical and chemical soil properties, topography, compression of soil, depth of soil and canopy cover was realized in 25 plots of 20 x 20m, where tree individuals, with circumference at breast height ≥15.7 cm were previously counted, measured and identified. The data were analysed by Mann-Withney test, non-parametric multivariate ANOVA (NPMANOVA, multivariate analysis (NMDS and indicator species analysis. In this small spatial scale there were two drainage classes, corresponding to well and moderately-drained soils, with environmental differences that determined the richness, the spatial partition of the tree community and the occurrence of indicator species. Thus, we conclude that in the study forest fragment soil drainage spatial variations were determinant in the floristic-structural heterogeneity observed in tree community.
Metal-Silicate Partitioning of Bi, In, and Cd as a Function of Temperature and Melt Composition
Marin, Nicole; Righter, K.; Danielson, L.; Pando, K.; Lee, C.
2013-01-01
The origin of volatile elements in the Earth, Moon and Mars is not known; however, several theories have been proposed based on volatile elements such as In, As, Se, Te and Zn which are in lower concentration in the Earth, Moon, and Mars than in chondrites. Explanations for these low concentrations are based on two contrasting theories for the origin of Earth: equilibrium core formation versus late accretion. One idea is that the volatiles were added during growth of the planets and Moon, and some mobilized into the metallic core while others stayed in the mantle (e.g., [1]). The competing idea is that they were added to the mantles after core formation had completed (e.g., [2]). Testing these ideas involves quantitative modeling which can only be performed after data is obtained on the systematic metal-silicate partitioning behavior of volatile elements with temperature, pressure and melt composition. Until now, such data for Bi, In, and Cd has been lacking. After conducting a series of high pressure, high temperature experiments, the metal-silicate partition coefficients of Bi, In, and Cd as a function of temperature and melt composition can be used to evaluate potential conditions under which terrestrial planets differentiated into core and mantle, and how they acquired volatiles.
Canonical Information Analysis
DEFF Research Database (Denmark)
Vestergaard, Jacob Schack; Nielsen, Allan Aasbjerg
2015-01-01
Canonical correlation analysis is an established multivariate statistical method in which correlation between linear combinations of multivariate sets of variables is maximized. In canonical information analysis introduced here, linear correlation as a measure of association between variables is...... replaced by the information theoretical, entropy based measure mutual information, which is a much more general measure of association. We make canonical information analysis feasible for large sample problems, including for example multispectral images, due to the use of a fast kernel density estimator...... for entropy estimation. Canonical information analysis is applied successfully to (1) simple simulated data to illustrate the basic idea and evaluate performance, (2) fusion of weather radar and optical geostationary satellite data in a situation with heavy precipitation, and (3) change detection in...
Bertot, Yves; Gonthier, Georges; Ould Biha, Sidi; Pasca, Ioana
2008-01-01
In this paper, we present an approach to describe uniformly iterated “big” operations and to provide lemmas that encapsulate all the commonly used reasoning steps on these constructs. We show that these iterated operations can be handled generically using the syntactic notation and canonical structure facilities provided by the Coq system. We then show how these canonical big operations played a crucial enabling role in the study of various parts of linear algebra and multi-dimensional real a...
Institute of Scientific and Technical Information of China (English)
LI Xiao-Dong; TANG Yong-Jian; CHENG Xin-Lu; ZHANG Hong
2011-01-01
The potential energies of H2 molecules with partially truncated and open cage C6o fullerenes,including Css,C55,C54(Ⅰ),C54(Ⅱ) and C46,are investigated by means of the density functional theory method.The energy barrier for one H2 molecule (with two postures) entering into the nanocage decreases from 435.59 (513.45)kcal/mol to 3.64 (-2.06) kcal/mol with the increase of the truncated pore.The grand canonical Monte Carlo simulations reveal that each nanocage can accommodate only one H2 molecule inside its cavity at both 77K and 298K.All the other H2 molecules are adsorbed round the truncated pores outside the nanocages.Exceptionally,the truncated C46 can store 2.28wt％ H2 molecules at 77K.Therefore,the truncating part of the C60 molecule may be a novel idea to explore C60 fullerene as a hydrogen storage material.Hydrogen is one of the clean and renewable energy carriers used to replace traditional fossil fuels,which have caused great negative effects on the environment.However,the main obstacle for the wide use of hydrogen is its dense and safe storage.[1-3] One proposed method is to physisorbe molecular hydrogen on porous materials.[4-6] Some studies found that metal organic frameworks have the potential to satisfy the goal of gravimetric density of 6wt％ hydrogen,[6-9]as set by the U.S.Department of Energy in 2010.However,it is unfortunate that the synthesis of these artificially designed frames is a tremendous obstacle.%The potential energies of H2 molecules with partially truncated and open cage C60 fullerenes, including C58, C55, C54(I), C54(I) and C46, are investigated by means of the density functional theory method. The energy barrier for one H2 molecule (with two postures) entering into the nanocage decreases from 435.59 (513.45) kcal/mol to 3.64 (-2.06) kcal/mol with the increase of the truncated pore. The grand canonical Monte Carlo simulations reveal that each nanocage can accommodate only one H2 molecule inside its cavity at both 77 K and 298 K. All
Ball, Joseph A
2011-01-01
We develop a $d$-variable analog of the two-component de Bran-ges-Rovnyak reproducing kernel Hilbert space associated with a Schur-class function on the unit disk. In this generalization, the unit disk is replaced by the unit ball in $d$-dimensional complex Euclidean space, and the Schur class becomes the class of contractive multipliers on the Drury-Arveson space over the ball. We also develop some results on a model theory for commutative row contractions which are not necessarily completely noncoisometric (the case considered in earlier work of Bhattacharyya, Eschmeier and Sarkar)
Alba, David; Crater, Horace W.; Lusanna, Luca
2012-01-01
A new formulation of relativistic classical mechanics allows a revisiting of old unsolved problems in relativistic kinetic theory and in relativistic statistical mechanics. In particular a definition of the relativistic micro-canonical partition function is given strictly in terms of the Poincar\\'e generators of an interacting N-particle system both in the inertial and non-inertial rest frames. The non-relativistic limit allows a definition of both the inertial and non-inertial micro-canonica...
On Partitions of Goldbach's Conjecture
Woon, Max S. C.
2000-01-01
An approximate formula for the partitions of Goldbach's Conjecture is derived using Prime Number Theorem and a heuristic probabilistic approach. A strong form of Goldbach's conjecture follows in the form of a lower bounding function for the partitions of Goldbach's conjecture. Numerical computations suggest that the lower and upper bounding functions for the partitions satisfy a simple functional equation. Assuming that this invariant scaling property holds for all even integer $n$, the lower...
da Silva Neto, Antônio Marinho; Torini de Souza, Juliana Roberta; Romanello, Larissa; Cassago, Alexandre; Serrão, Vitor Hugo Balasco; DeMarco, Ricardo; Brandão-Neto, José; Garratt, Richard Charles; Pereira, Humberto D'Muniz
2016-06-01
Reports of Schistosoma mansoni strains resistant to praziquantel, the only therapeutic strategy available for the treatment of schistosomiasis, have motivated the scientific community towards the search for new possible therapies. Biochemical characterization of the parasite's metabolism is an essential component for the rational development of new therapeutic alternatives. One of the so far uncharacterized enzymes is uridine phosphorylase (UP) (EC 2.4.2.3), for which the parasite genome presents two isoforms (SmUPa and SmUPb) that share 92% sequence identity. In this paper, we present crystal structures for SmUPa and SmUPb in their free states as well as bound to different ligands. This we have complemented by enzyme kinetic characterization and phylogenetic analyses. Both enzymes present an overall fold and active site structure similar to other known UPs. The kinetic analyses showed conclusively that SmUPa is a regular uridine phosphorylase but by contrast SmUPb presented no detectable activity. This is particularly noteworthy given the high level of sequence identity between the two isoforms and is probably the result of the significant differences observed for SmUPb in the vicinity of the active site itself, suggesting that it is not a UP at all. On the other hand, it was not possible to identify an alternative function for SmUPb, although our phylogenetic analyses and expression data suggest that SmUPb is still functional and plays a role in parasite metabolism. The unusual UPb isoform may open up new opportunities for understanding unique features of S. mansoni metabolism. PMID:26898674
Ragni, Mirco; Bitencourt, Ana Carla P.; Prudente, Frederico V.; Barreto, Patricia R. P.; Posati, Tamara
2016-03-01
A study of the umbrella motion of the methyl cation, radical, and anion molecules is presented. This is the floppiest mode of vibration of all three species and its characterization is of fundamental importance for understanding their reactivity. Minimum Energy Paths of the umbrella motions according to the hyperspherical treatment were obtained, by single point calculations, at the CCSD(T)/aug-cc-pVQT level of theory in the Born-Oppenheimer approximation. These energy profiles permit us to calculate the vibrational levels through the Hyperquantization algorithm, which is shown appropriated for the description of the umbrella motion of these three molecules. The adiabatic electron affinity and ionization potentials were estimated to good accuracy. Partition functions are also calculated in order to obtain information on the reaction rates involving these groups.
International Nuclear Information System (INIS)
In order to get a clue to understanding the volume-dependence of vortex free energy (which is defined as the ratio of the twisted against the untwisted partition function), we investigate the relation between vortex free energies defined on lattices of different sizes. An equality is derived through a simple calculation which equates a general linear combination of vortex free energies defined on a lattice to that on a smaller lattice. The couplings in the denominator and in the numerator however shows a discrepancy, and we argue that it vanishes in the thermodynamic limit. Comparison between our result and the work of Tomboulis is also presented. In the appendix we carefully examine the proof of quark confinement by Tomboulis and summarize its loopholes
International Nuclear Information System (INIS)
Based on the ab initio molecular orbital theory at the HF/6-31G(d) level, the effect of hydration on the reduced partition function ratio (RPFR) of the boric acid molecule (B(OH)3) was evaluated in order to better understand boron isotope fractionation observed in aqueous systems. The B(OH)3(H2O)n species with n up to 12 were considered and their geometry optimization and RPFR calculations were carried out. It was induced that hydration decreased the RPFR of B(OH)3 and the degree of decrease in ln(RPFR) was ca. 1.5%, which was nearly equivalent to that of B(OH)4-. (author)
Liu, X.; Lee, C. K.; Fan, S. C.
Amongst the various approaches of `meshless' method, the Partition-of-unity concept married with the traditional finite-element method, namely PUFEM, has emerged to be competitive in solving the boundary-value problems. It inherits most of the advantages from both techniques except that the beauty of being `meshless' vanishes. This paper presents an alternative approach to solve singular boundary-value problems. It follows the basic PUFEM procedures. The salient feature is to enhance the quality of the influence functions, either over one single nodal cover or multi-nodal-covers. In the vicinity of the singularity, available asymptotic analytical solution is employed to enrich the influence function. The beauty of present approach is that it facilitates easy replacement of the influence functions. In other words, it favors the `influence-function refinement' procedure in a bid to search for more accurate solutions. It is analogous to the `p-version refinement' in the traditional finite-element procedures. The present approach can yield very accurate solution without adopting refined meshes. As a result, the quantities around the singularity can be evaluated directly once the nodal values are solved. No additional post-processing is needed. Firstly, the formulation of the present PUFEM approach is described. Subsequently, illustrative examples show the application to three classical singular benchmark problems having various orders of singularity. Results obtained through mesh refinements, single-nodal-cover refinements or multi-nodal-cover refinements are compared.
q-series, elliptic curves, and odd values of the partition function
Nicholas Eriksson
1999-01-01
Let p(n) be the number of partitions of an integer n. Euler proved the following recurrence for p(n): p(n)=Ã¢ÂˆÂ‘k=1Ã¢ÂˆÂž(Ã¢ÂˆÂ’1)k+1(p(nÃ¢ÂˆÂ’ÃÂ‰(k))+p(nÃ¢ÂˆÂ’ÃÂ‰(Ã¢ÂˆÂ’k))),Ã¢Â€Â‰Ã¢Â€Â‰Ã¢Â€Â‰Ã¢Â€Â‰Ã¢Â€Â‰Ã¢Â€Â‰Ã¢Â€Â‰Ã¢Â€Â‰Ã¢Â€Â‰Ã¢Â€Â‰Ã¢Â€Â‰Ã¢Â€Â‰Ã¢Â€Â‰Ã¢Â€Â‰Ã¢Â€Â‰Ã¢Â€Â‰Ã¢Â€Â‰Ã¢Â€Â‰Ã¢Â€Â‰Ã¢Â€Â‰Ã¢Â€Â‰Ã¢Â€Â‰Ã¢Â€Â‰Ã¢Â€Â‰Ã¢Â€Â‰Ã¢Â€Â‰Ã¢Â€Â‰Ã¢Â€Â‰Ã¢Â€Â‰Ã¢Â€Â‰Ã¢Â€Â‰Ã¢Â€Â‰Ã¢Â€Â‰Ã¢Â€Â‰Ã¢Â€Â‰Ã¢Â€Â‰Ã¢Â€Â‰Ã¢Â€Â‰Ã¢Â€Â‰Ã¢Â€Â‰(*) where ÃÂ‰(k)=(3kÃ¢Â€Â‰2+k)/2. In view of Euler's result, one sees that it is ...
Canonical affordances in context
Directory of Open Access Journals (Sweden)
Alan Costall
2012-12-01
Full Text Available James Gibson’s concept of affordances was an attempt to undermine the traditional dualism of the objective and subjective. Gibson himself insisted on the continuity of “affordances in general” and those attached to human artifacts. However, a crucial distinction needs to be drawn between “affordances in general” and the “canonical affordances” that are connected primarily to artifacts. Canonical affordances are conventional and normative. It is only in such cases that it makes sense to talk of the affordance of the object. Chairs, for example, are for sitting-on, even though we may also use them in many other ways. A good deal of confusion has arisen in the discussion of affordances from (1 the failure to recognize the normative status of canonical affordances and (2 then generalizing from this special case.
Hori method for generalized canonical systems
da Silva Fernandes, Sandro
2009-01-01
In this paper, some special features on the canonical version of Hori method, when it is applied to generalized canonical systems (systems of differential equations described by a Hamiltonian function linear in the momenta), are presented. Two different procedures, based on a new approach for the integration theory recently presented for the canonical version, are proposed for determining the new Hamiltonian and the generating function for systems whose differential equations for the coordinates describe a periodic system with one fast phase. These procedures are equivalent and they are directly related to the canonical transformations defined by the general solution of the integrable kernel of the Hamiltonian. They provide the same near-identity transformation for the coordinates obtained through the non-canonical version of Hori method. It is also shown that these procedures are connected to the classic averaging principle through a canonical transformation. As examples, asymptotic solutions of a non-linear oscillations problem and of the elliptic perturbed problem are discussed.
Receiving the non-Orthodox: A historical study of Greek Orthodox canon law
Heith-Stade, David
2010-01-01
This article analyzes the development of the practice for receiving non-Orthodox in Greek Orthodox canon law. The main argument is that the development of this canonical institution was influenced by a pneumatological realist ecclesiology. This historical study of the development of a canonical institution will shed light on how Greek Orthodox canon law has functioned in practice.
Hierarchical Partitioning of Metazoan Protein Conservation Profiles Provides New Functional Insights
Witztum, Jonathan; Persi, Erez; Horn, David; Pasmanik-Chor, Metsada; Chor, Benny
2014-01-01
The availability of many complete, annotated proteomes enables the systematic study of the relationships between protein conservation and functionality. We explore this question based solely on the presence or absence of protein homologues (a.k.a. conservation profiles). We study 18 metazoans, from two distinct points of view: the human's and the fly's. Using the GOrilla gene ontology (GO) analysis tool, we explore functional enrichment of the “universal proteins”, those with homologues in al...
Luo, Chongliang; Liu, Jin; Dey, Dipak K; Chen, Kun
2016-07-01
In many fields, multi-view datasets, measuring multiple distinct but interrelated sets of characteristics on the same set of subjects, together with data on certain outcomes or phenotypes, are routinely collected. The objective in such a problem is often two-fold: both to explore the association structures of multiple sets of measurements and to develop a parsimonious model for predicting the future outcomes. We study a unified canonical variate regression framework to tackle the two problems simultaneously. The proposed criterion integrates multiple canonical correlation analysis with predictive modeling, balancing between the association strength of the canonical variates and their joint predictive power on the outcomes. Moreover, the proposed criterion seeks multiple sets of canonical variates simultaneously to enable the examination of their joint effects on the outcomes, and is able to handle multivariate and non-Gaussian outcomes. An efficient algorithm based on variable splitting and Lagrangian multipliers is proposed. Simulation studies show the superior performance of the proposed approach. We demonstrate the effectiveness of the proposed approach in an [Formula: see text] intercross mice study and an alcohol dependence study. PMID:26861909
Gregory, Jesse F; DeRatt, Barbara N; Rios-Avila, Luisa; Ralat, Maria; Stacpoole, Peter W
2016-07-01
The transsulfuration pathway (TS) acts in sulfur amino acid metabolism by contributing to the regulation of cellular homocysteine, cysteine production, and the generation of H2S for signaling functions. Regulation of TS pathway kinetics involves stimulation of cystathionine β-synthase (CBS) by S-adenosylmethionine (SAM) and oxidants such as H2O2, and by Michaelis-Menten principles whereby substrate concentrations affect reaction rates. Although pyridoxal phosphate (PLP) serves as coenzyme for both CBS and cystathionine γ-lyase (CSE), CSE exhibits much greater loss of activity than CBS during PLP insufficiency. Thus, cellular and plasma cystathionine concentrations increase in vitamin B6 deficiency mainly due to the bottleneck caused by reduced CSE activity. Because of the increase in cystathionine, the canonical production of cysteine (homocysteine → cystathionine → cysteine) is largely maintained even during vitamin B6 deficiency. Typical whole body transsulfuration flux in humans is 3-7 μmol/h per kg body weight. The in vivo kinetics of H2S production via side reactions of CBS and CSE in humans are unknown but they have been reported for cultured HepG2 cells. In these studies, cells exhibit a pronounced reduction in H2S production capacity and rates of lanthionine and homolanthionine synthesis in deficiency. In humans, plasma concentrations of lanthionine and homolanthionine exhibit little or no mean change due to 4-wk vitamin B6 restriction, nor do they respond to pyridoxine supplementation of subjects in chronically low-vitamin B6 status. Wide individual variation in responses of the H2S biomarkers to such perturbations of human vitamin B6 status suggests that the resulting modulation of H2S production may have physiological consequences in a subset of people. Supported by NIH grant DK072398. This paper refers to data from studies registered at clinicaltrials.gov as NCT01128244 and NCT00877812. PMID:26765812
Zheng, Jingjing; Mielke, Steven L.; Clarkson, Kenneth L.; Truhlar, Donald G.
2012-08-01
We present a Fortran program package, MSTor, which calculates partition functions and thermodynamic functions of complex molecules involving multiple torsional motions by the recently proposed MS-T method. This method interpolates between the local harmonic approximation in the low-temperature limit, and the limit of free internal rotation of all torsions at high temperature. The program can also carry out calculations in the multiple-structure local harmonic approximation. The program package also includes six utility codes that can be used as stand-alone programs to calculate reduced moment of inertia matrices by the method of Kilpatrick and Pitzer, to generate conformational structures, to calculate, either analytically or by Monte Carlo sampling, volumes for torsional subdomains defined by Voronoi tessellation of the conformational subspace, to generate template input files, and to calculate one-dimensional torsional partition functions using the torsional eigenvalue summation method. Catalogue identifier: AEMF_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEMF_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 77 434 No. of bytes in distributed program, including test data, etc.: 3 264 737 Distribution format: tar.gz Programming language: Fortran 90, C, and Perl Computer: Itasca (HP Linux cluster, each node has two-socket, quad-core 2.8 GHz Intel Xeon X5560 “Nehalem EP” processors), Calhoun (SGI Altix XE 1300 cluster, each node containing two quad-core 2.66 GHz Intel Xeon “Clovertown”-class processors sharing 16 GB of main memory), Koronis (Altix UV 1000 server with 190 6-core Intel Xeon X7542 “Westmere” processors at 2.66 GHz), Elmo (Sun Fire X4600 Linux cluster with AMD Opteron cores), and Mac Pro (two 2.8 GHz Quad-core Intel Xeon
Application of Loreau & Hector's (2001) partitioning method to complex functional traits
Grossiord, Charlotte; Granier, André; Gessler, Arthur; Scherer-Lorenzen, Michael; Pollastrini, Martina; Bonal, Damien
2013-01-01
In 2001, Loreau and Hector proposed a method to calculate the effect of biodiversity on ecosystem-level properties that distinguished selection effects (SE) from complementarity effects (CE). The approach was designed and has been widely used for the study of yield in mixed-species situations taking into account the relative abundance of each species in ecosystem-level yield. However, complex functional traits commonly used to integrate ecosystem-level properties that cannot be analysed like ...
The canonical and grand canonical models for nuclear multifragmentation
Indian Academy of Sciences (India)
G Chaudhuri; S Das Gupta
2010-08-01
Many observables seen in intermediate energy heavy-ion collisions can be explained on the basis of statistical equilibrium. Calculations based on statistical equilibrium can be implemented in microcanonical ensemble, canonical ensemble or grand canonical ensemble. This paper deals with calculations with canonical and grand canonical ensembles. A recursive relation developed recently allows calculations with arbitrary precision for many nuclear problems. Calculations are done to study the nature of phase transition in nuclear matter.
Quaternion Linear Canonical Transform Application
Bahri, Mawardi
2015-01-01
Quaternion linear canonical transform (QLCT) is a generalization of the classical linear canonical transfom (LCT) using quaternion algebra. The focus of this paper is to introduce an application of the QLCT to study of generalized swept-frequency filter
Realizations of the Canonical Representation
Indian Academy of Sciences (India)
M K Vemuri
2008-02-01
A characterisation of the maximal abelian subalgebras of the bounded operators on Hilbert space that are normalised by the canonical representation of the Heisenberg group is given. This is used to classify the perfect realizations of the canonical representation.
Directory of Open Access Journals (Sweden)
J. Park
2010-06-01
Full Text Available An energy-conservative metric based on the discrete wavelet transform is applied to assess the relative energy distribution of extreme sea level events across different temporal scales. The metric is applied to coastal events at Key West and Pensacola Florida as a function of two Atlantic Multidecadal Oscillation (AMO regimes. Under AMO warm conditions there is a small but significant redistribution of event energy from nearly static into more dynamic (shorter duration timescales at Key West, while at Pensacola the AMO-dependent changes in temporal event behaviour are less pronounced. Extreme events with increased temporal dynamics might be consistent with an increase in total energy of event forcings which may be a reflection of more energetic storm events during AMO warm phases. As dynamical models mature to the point of providing regional climate index predictability, coastal planners may be able to consider such temporal change metrics in planning scenarios.
Directory of Open Access Journals (Sweden)
J. Park
2010-03-01
Full Text Available An energy-conservative metric based on the discrete wavelet transform is applied to assess the relative energy distribution of non-stationary extreme sea level events across different temporal scales. The metric is applied to coastal events at Key West and Pensacola Florida as a function of two Atlantic Multidecadal Oscillation (AMO regimes. Under AMO warm conditions there is a small but significant redistribution of event energy from nearly static into more dynamic timescales at Key West, while at Pensacola the AMO-dependent changes in temporal event behaviour are less pronounced. Extreme events with increased temporal dynamics are consistent with an increase in total energy of event forcings which may be a reflection of more energetic storm events during AMO warm phases. As dynamical models mature to the point of providing regional climate index predictability, coastal planners may be able to consider such temporal change metrics in planning scenarios.
Rhythmic canons and modular tiling
Caure, Hélianthe
2016-01-01
This thesis is a contribution to the study of modulo p tiling. Many mathematical and computational tools were used for the study of rhythmic tiling canons. Recent research has mainly focused in finding tiling without inner periodicity, being called Vuza canons. Those canons are a constructive basis for all rhythmic tiling canons, however, they are really difficult to obtain. Best current method is a brut force exploration that, despite a few recent enhancements, is exponential. Many technics ...
Directory of Open Access Journals (Sweden)
Tom O Delmont
2015-10-01
Full Text Available Antarctica polynyas support intense phytoplankton blooms, impacting their environment by a substantial depletion of inorganic carbon and nutrients. These blooms are dominated by the colony-forming haptophyte Phaeocystis antarctica and they are accompanied by a distinct bacterial population. Yet, the ecological role these bacteria may play in P. antarctica blooms awaits elucidation of their functional gene pool and of the geochemical activities they support. Here, we report on a metagenome (῀160 million reads analysis of the microbial community associated with a P. antarctica bloom event in the Amundsen Sea polynya (West Antarctica. Genomes of the most abundant Bacteroidetes and Proteobacteria populations have been reconstructed and a network analysis indicates a strong functional partitioning of these bacterial taxa. Three of them (SAR92, and members of the Oceanospirillaceae and Cryomorphaceae are found in close association with P. antarctica colonies. Distinct features of their carbohydrate, nitrogen, sulfur and iron metabolisms may serve to support mutualistic relationships with P. antarctica. The SAR92 genome indicates a specialization in the degradation of fatty acids and dimethylsulfoniopropionate (compounds released by P. antarctica into dimethyl sulfide, an aerosol precursor. The Oceanospirillaceae genome carries genes that may enhance algal physiology (cobalamin synthesis. Finally, the Cryomorphaceae genome is enriched in genes that function in cell or colony invasion. A novel pico-eukaryote, Micromonas related genome (19.6 Mb, ~94% completion was also recovered. It contains the gene for an anti-freeze protein, which is lacking in Micromonas at lower latitudes. These draft genomes are representative for abundant microbial taxa across the Southern Ocean surface.
Choy, Jaeyoo
2016-08-01
Let K be the compact Lie group USp(N / 2) or SO(N , R) . Let MnK be the moduli space of framed K-instantons over S4 with the instanton number n. By Donaldson (1984), MnK is endowed with a natural scheme structure. It is a Zariski open subset of a GIT quotient of μ-1(0) , where μ is a holomorphic moment map such that μ-1(0) consists of the ADHM data. The purpose of the paper is to study the geometric properties of μ-1(0) and its GIT quotient, such as complete intersection, irreducibility, reducedness and normality. If K = USp(N / 2) then μ is flat and μ-1(0) is an irreducible normal variety for any n and even N. If K = SO(N , R) the similar results are proven for low n and N. As an application one can obtain a mathematical interpretation of the K-theoretic Nekrasov partition function of Nekrasov and Shadchin (2004).
Balawender, Robert
2009-01-01
A unified formulation of the equilibrium state of a many-electron system in terms of an ensemble (mixed-state) density matrix, which applies the maximum entropy principle combined with the use of Massieu-Planck function, is presented. The properties of the characteristic functionals for macrocanonical ensemble are established. Their extension to other ensembles is accomplished via a Legendre transform. The relations between equilibrium states defined by a formal mathematical procedure and by criteria adopted for traditional (Gibbs, Helmholtz) potentials are investigated using Massieu-Planck transform. The preeminence of the Massieu-Planck function over the traditional thermodynamic potentials is discussed in detail on an example of their second derivatives. Introduced functions are suitable for application to the extensions of the density functional theory, both at finite and zero temperatures.
Vortex partition functions, wall crossing and equivariant Gromov-Witten invariants
Bonelli, Giulio; Tanzini, Alessandro; Vasko, Petr
2013-01-01
In this paper we identify the problem of equivariant vortex counting in a (2,2) supersymmetric two dimensional quiver gauged linear sigma model with that of computing the equivariant Gromov-Witten invariants of the GIT quotient target space determined by the quiver. We provide new contour integral formulae for the I and J-functions encoding the equivariant quantum cohomology of the target space. Its chamber structure is shown to be encoded in the analytical properties of the integrand. This is explained both via general arguments and by checking several key cases. We show how several results in equivariant Gromov-Witten theory follow just by deforming the integration contour. In particular we apply our formalism to compute Gromov-Witten invariants of the C^3/Z_n orbifold and of the Uhlembeck (partial) compactification of the moduli space of instantons on C^2. Moreover, we analyse dualities of quantum cohomology rings of holomorphic vector bundles over Grassmannians, which are relevant to BPS Wilson loop algeb...
Canonical transformations and Hamiltonian evolutionary systems
International Nuclear Information System (INIS)
In many Lagrangian field theories, one has a Poisson bracket defined on the space of local functionals. We find necessary and sufficient conditions for a transformation on the space of local functionals to be canonical in three different cases. These three cases depend on the specific dimensions of the vector bundle of the theory and the associated Hamiltonian differential operator. We also show how a canonical transformation transforms a Hamiltonian evolutionary system and its conservation laws. Finally, we illustrate these ideas with three examples.
Revisiting Canonical Quantization
Klauder, John R.
2012-01-01
Conventional canonical quantization procedures directly link various c-number and q-number quantities. Here, we advocate a different association of classical and quantum quantities that renders classical theory a natural subset of quantum theory with \\hbar>0, in conformity with the real world wherein nature has chosen \\hbar>0 rather than \\hbar=0. While keeping the good results of conventional procedures, some examples are presented for which the new procedures offer better results than conven...
Canonical Infinitesimal Deformations
Ran, Ziv
1998-01-01
This paper gives a canonical construction, in terms of additive cohomological functors, of the universal formal deformation of a compact complex manifold without vector fields (more generally of a faithful $g$-module, where $g$ is a sheaf of Lie algebras without sections). The construction is based on a certain (multivariate) Jacobi complex $J(g)$ associatd to $g$: indeed ${\\mathbb C}\\oplus {\\mathbb H}^0(J(g))^*$ is precisely the base ring of the universal deformation.
Bilal, Adel; Leduc, Laetitia
2015-07-01
We study two-dimensional quantum gravity on arbitrary genus Riemann surfaces in the Kähler formalism where the basic quantum field is the (Laplacian of the) Kähler potential. We do a careful first-principles computation of the fixed-area partition function Z [ A ] up to and including all two-loop contributions. This includes genuine two-loop diagrams as determined by the Liouville action, one-loop diagrams resulting from the non-trivial measure on the space of metrics, as well as one-loop diagrams involving various counterterm vertices. Contrary to what is often believed, several such counterterms, in addition to the usual cosmological constant, do and must occur. We consistently determine the relevant counterterms from a one-loop computation of the full two-point Green's function of the Kähler field. Throughout this paper we use the general spectral cutoff regularization developed recently and which is well-suited for multi-loop computations on curved manifolds. At two loops, while all "unwanted" contributions to ln (Z [ A ] / Z [A0 ]) correctly cancel, it appears that the finite coefficient of ln (A /A0) does depend on the finite part of a certain counterterm coefficient, i.e. on the finite renormalization conditions one has to impose. There exists a choice that reproduces the famous KPZ-scaling, but it seems to be only one consistent choice among others. Maybe, this hints at the possibility that other renormalization conditions could eventually provide a way to circumvent the famous c = 1 barrier.
Directory of Open Access Journals (Sweden)
Adel Bilal
2015-07-01
Full Text Available We study two-dimensional quantum gravity on arbitrary genus Riemann surfaces in the Kähler formalism where the basic quantum field is the (Laplacian of the Kähler potential. We do a careful first-principles computation of the fixed-area partition function Z[A] up to and including all two-loop contributions. This includes genuine two-loop diagrams as determined by the Liouville action, one-loop diagrams resulting from the non-trivial measure on the space of metrics, as well as one-loop diagrams involving various counterterm vertices. Contrary to what is often believed, several such counterterms, in addition to the usual cosmological constant, do and must occur. We consistently determine the relevant counterterms from a one-loop computation of the full two-point Green's function of the Kähler field. Throughout this paper we use the general spectral cutoff regularization developed recently and which is well-suited for multi-loop computations on curved manifolds. At two loops, while all “unwanted” contributions to ln(Z[A]/Z[A0] correctly cancel, it appears that the finite coefficient of ln(A/A0 does depend on the finite part of a certain counterterm coefficient, i.e. on the finite renormalization conditions one has to impose. There exists a choice that reproduces the famous KPZ-scaling, but it seems to be only one consistent choice among others. Maybe, this hints at the possibility that other renormalization conditions could eventually provide a way to circumvent the famous c=1 barrier.
Mielke, Steven L.; Truhlar, Donald G.
2015-01-01
We present an improved version of our "path-by-path" enhanced same path extrapolation scheme for Feynman path integral (FPI) calculations that permits rapid convergence with discretization errors ranging from O(P-6) to O(P-12), where P is the number of path discretization points. We also present two extensions of our importance sampling and stratified sampling schemes for calculating vibrational-rotational partition functions by the FPI method. The first is the use of importance functions for dihedral angles between sets of generalized Jacobi coordinate vectors. The second is an extension of our stratification scheme to allow some strata to be defined based only on coordinate information while other strata are defined based on both the geometry and the energy of the centroid of the Feynman path. These enhanced methods are applied to calculate converged partition functions by FPI methods, and these results are compared to ones obtained earlier by vibrational configuration interaction (VCI) calculations, both calculations being for the Jordan-Gilbert potential energy surface. The earlier VCI calculations are found to agree well (within ˜1.5%) with the new benchmarks. The FPI partition functions presented here are estimated to be converged to within a 2σ statistical uncertainty of between 0.04% and 0.07% for the given potential energy surface for temperatures in the range 300-3000 K and are the most accurately converged partition functions for a given potential energy surface for any molecule with five or more atoms. We also tabulate free energies, enthalpies, entropies, and heat capacities.
Energy Technology Data Exchange (ETDEWEB)
Mielke, Steven L., E-mail: slmielke@gmail.com, E-mail: truhlar@umn.edu; Truhlar, Donald G., E-mail: slmielke@gmail.com, E-mail: truhlar@umn.edu [Department of Chemistry, Chemical Theory Center, and Supercomputing Institute, University of Minnesota, 207 Pleasant St. S.E., Minneapolis, Minnesota 55455-0431 (United States)
2015-01-28
We present an improved version of our “path-by-path” enhanced same path extrapolation scheme for Feynman path integral (FPI) calculations that permits rapid convergence with discretization errors ranging from O(P{sup −6}) to O(P{sup −12}), where P is the number of path discretization points. We also present two extensions of our importance sampling and stratified sampling schemes for calculating vibrational–rotational partition functions by the FPI method. The first is the use of importance functions for dihedral angles between sets of generalized Jacobi coordinate vectors. The second is an extension of our stratification scheme to allow some strata to be defined based only on coordinate information while other strata are defined based on both the geometry and the energy of the centroid of the Feynman path. These enhanced methods are applied to calculate converged partition functions by FPI methods, and these results are compared to ones obtained earlier by vibrational configuration interaction (VCI) calculations, both calculations being for the Jordan–Gilbert potential energy surface. The earlier VCI calculations are found to agree well (within ∼1.5%) with the new benchmarks. The FPI partition functions presented here are estimated to be converged to within a 2σ statistical uncertainty of between 0.04% and 0.07% for the given potential energy surface for temperatures in the range 300–3000 K and are the most accurately converged partition functions for a given potential energy surface for any molecule with five or more atoms. We also tabulate free energies, enthalpies, entropies, and heat capacities.
Directory of Open Access Journals (Sweden)
Agapitos N. Hatzinikitas
2015-01-01
Full Text Available We study the asymptotic behavior of the free partition function in the t→0+ limit for a diffusion process which consists of d-independent, one-dimensional, symmetric, 2s-stable processes in a hyperrectangular cavity K⊂Rd with an absorbing boundary. Each term of the partition function for this polyhedron in d-dimensions can be represented by a quermassintegral and the geometrical information conveyed by the eigenvalues of the fractional Dirichlet Laplacian for this solvable model is now transparent. We also utilize the intriguing method of images to solve the same problem, in one and two dimensions, and recover identical results to those derived in the previous analysis.
Feng, Genfeng; Liu, Wei; Peng, Yuxin; Zhao, Bo; Huang, Wei; Dai, Yafei
2016-07-28
The cavity of a [2+3] organic molecular cage was partitioned and functionalized by inserting inner-directed P[double bond, length as m-dash]O bonds, which shows CO2 capture and CH4 exclusion due to the size-matching and polarity effects. Computational results demonstrate that the successful segmentation via polar P[double bond, length as m-dash]O bonds facilitates the CO2 molecules to reside selectively inside the cavity. PMID:27356151
Partitions with Initial Repetitions
Institute of Scientific and Technical Information of China (English)
George E. ANDREWS
2009-01-01
A variety of interesting connections with modular forms, mock theta functions and Rogers-Ramanujan type identities arise in consideration of partitions in which the smaller integers are repeated as summands more often than the larger summands. In particular, this concept leads to new interpre-tations of the Rogers-Selberg identities and Bailey's modulus 9 identities.
Canonical Quantization of Higher-Order Lagrangians
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Khaled I. Nawafleh
2011-01-01
Full Text Available After reducing a system of higher-order regular Lagrangian into first-order singular Lagrangian using constrained auxiliary description, the Hamilton-Jacobi function is constructed. Besides, the quantization of the system is investigated using the canonical path integral approximation.
Canonical Ensemble Model for Black Hole Radiation
Indian Academy of Sciences (India)
Jingyi Zhang
2014-09-01
In this paper, a canonical ensemble model for the black hole quantum tunnelling radiation is introduced. In this model the probability distribution function corresponding to the emission shell is calculated to second order. The formula of pressure and internal energy of the thermal system is modified, and the fundamental equation of thermodynamics is also discussed.
Bonduelle, M
1987-01-01
The Canon Law (Codex Iuris Canonici), promulgated in 1917, was a classification of laws and jurisprudence which ruled the early Church, governed the ecclesiastical condition of Roman Church until its reorganisation in 1983. It forbade to be ordained or to exercise orders already received to "those who are or were epileptics either not quite in their right mind or possessed by the Evil One". All the context and in particular the paragraph which treated of bodily lacks, indicated that between these three conditions, there was juxtaposition and no confusion. The texts specified the foundations of these dispositions, not in a malefic view of epilepsy inherited from Morbus Sacer of Antiquity, but in decency and on account of risk incured by Eucharist in case of fit. Some derogations could attenuate the severity of these dispositions--as jurisprudence had taken progresses of Epileptology and therapeutics into consideration. In the new Code of Canon Law (1983) physical disabilities were removed from the text and also possessed evil and epilepsy, the only impediment being "insanity or other psychic defect" appreciation of which is done by experts. Concerning poorly controlled epilepsies, we believe that experts will be allowed to express their opinion and a new jurisprudence will make up for the silence of the law. PMID:3310183
Physical states in the canonical tensor model from the perspective of random tensor networks
Narain, Gaurav; Sato, Yuki
2014-01-01
Tensor models, generalization of matrix models, are studied aiming for quantum gravity in dimensions larger than two. Among them, the canonical tensor model is formulated as a totally constrained system with first-class constraints, the algebra of which resembles the Dirac algebra of general relativity. When quantized, the physical states are defined to be vanished by the quantized constraints. In explicit representations, the constraint equations are a set of partial differential equations for physical wave-functions, which do not seem straightforward to solve due to their non-linear character. In this paper, after providing some explicit solutions for N = 2,3, we show that certain scale-free integration of partition functions of statistical systems on random networks, or random tensor networks more generally, provides a series of solutions for general N. Then, by generalizing this form, we also obtain various solutions for general N. Moreover, we show that the solutions for the cases with a cosmological con...
Czech Academy of Sciences Publication Activity Database
Gavinsky, Dmitry; Pudlák, Pavel
Dagstuhl: Schloss Dagstuhl, Leibniz-Zentrum für Informatik, 2014 - (Mayr, E.; Portier, N.), s. 325-336. (Leibniz International Proceedings in Informatics. 25). ISBN 978-3-939897-65-1. ISSN 1868-8969. [International Symposium on Theoretical Aspects of Computer Science (STACS 2014), /31./. Lyon (FR), 05.03.2014-08.03.2014] R&D Projects: GA ČR GBP202/12/G061 Institutional support: RVO:67985840 Keywords : partitions * expanders * random graphs Subject RIV: BA - General Mathematics http://drops.dagstuhl.de/opus/volltexte/2014/4468/
Schell, David George
2008-01-01
The matrix partition problem has been of recent interest in graph theory. Matrix partitions generalize the study of graph colourings and homomorphisms. Many well-known graph partition problems can be stated in terms of matrices. For example skew partitions, split partitions, homogeneous sets, clique-cutsets, stable-cutsets and k-colourings can all be modeled as matrix partitions. For each matrix partition problem there is an equivalent trigraph H-colouring problem. We show a ‘dichotomy’ for t...
Regularized Generalized Canonical Correlation Analysis
Tenenhaus, Arthur; Tenenhaus, Michel
2011-01-01
Regularized generalized canonical correlation analysis (RGCCA) is a generalization of regularized canonical correlation analysis to three or more sets of variables. It constitutes a general framework for many multi-block data analysis methods. It combines the power of multi-block data analysis methods (maximization of well identified criteria) and…
Canonical correlations between chemical and energetic characteristics of lignocellulosic wastes
Directory of Open Access Journals (Sweden)
Thiago de Paula Protásio
2012-09-01
Full Text Available Canonical correlation analysis is a statistical multivariate procedure that allows analyzing linear correlation that may exist between two groups or sets of variables (X and Y. This paper aimed to provide canonical correlation analysis between a group comprised of lignin and total extractives contents and higher heating value (HHV with a group of elemental components (carbon, hydrogen, nitrogen and sulfur for lignocellulosic wastes. The following wastes were used: eucalyptus shavings; pine shavings; red cedar shavings; sugar cane bagasse; residual bamboo cellulose pulp; coffee husk and parchment; maize harvesting wastes; and rice husk. Only the first canonical function was significant, but it presented a low canonical R². High carbon, hydrogen and sulfur contents and low nitrogen contents seem to be related to high total extractives contents of the lignocellulosic wastes. The preliminary results found in this paper indicate that the canonical correlations were not efficient to explain the correlations between the chemical elemental components and lignin contents and higher heating values.
Faribault, Alexandre; Tschirhart, Hugo; Muller, Nicolas
2016-05-01
In this work we present a determinant expression for the domain-wall boundary condition partition function of rational (XXX) Richardson-Gaudin models which, in addition to N-1 spins \\frac{1}{2}, contains one arbitrarily large spin S. The proposed determinant representation is written in terms of a set of variables which, from previous work, are known to define eigenstates of the quantum integrable models belonging to this class as solutions to quadratic Bethe equations. Such a determinant can be useful numerically since systems of quadratic equations are much simpler to solve than the usual highly nonlinear Bethe equations. It can therefore offer significant gains in stability and computation speed.
Energy Technology Data Exchange (ETDEWEB)
Foda, Omar; Wheeler, Michael [Department of Mathematics and Statistics, University of Melbourne, Parkville, Victoria 3010 (Australia)
2007-01-15
Using BKP neutral fermions, we derive a product expression for the generating function of volume-weighted plane partitions that satisfy two conditions. If we call a set of adjacent equal height-h columns, h > 0, an h-path, then 1. Every h-path can assume one of two possible colours. 2. There is a unique way to move along an h-path from any column to another.
Foda, O.; Wheeler, M.
2006-01-01
Using BKP neutral fermions, we derive a product expression for the generating function of volume-weighted plane partitions that satisfy two conditions. If we call a set of adjacent equal height-h columns, h > 0, an h-path, then 1. Every h-path can assume one of two possible colours. 2. There is a unique way to move along an h-path from any column to another.
International Nuclear Information System (INIS)
Using BKP neutral fermions, we derive a product expression for the generating function of volume-weighted plane partitions that satisfy two conditions. If we call a set of adjacent equal height-h columns, h > 0, an h-path, then 1. Every h-path can assume one of two possible colours. 2. There is a unique way to move along an h-path from any column to another
Canonical versus grand canonical treatment of the conservation laws
International Nuclear Information System (INIS)
The differences between the canonical and the grand canoncial treatment of the conservation laws in the relativistic statistical thermodynamics are discussed. The possible implications on the thermodynamics description of hadronic matter created in particle or ion collisions are considered
Solve the partitioning problem by sticker model in DNA computing
Institute of Scientific and Technical Information of China (English)
QU Huiqin; LU Mingming; ZHU Hong
2004-01-01
The aim of this work is to solve the partitioning problem, the most canonical NP-complete problem containing numerical parameters, within the sticker model of DNA computing. We firstly design a parallel program for addition, and then give a program to calculate the subset sums of a set. At last, a program for partitioning is given, which contains the former programs. Furthermore, the correctness of each program is proved in this paper.
Canonical cortical circuits: current evidence and theoretical implications
Directory of Open Access Journals (Sweden)
Capone F
2016-04-01
Full Text Available Fioravante Capone,1,2 Matteo Paolucci,1,2 Federica Assenza,1,2 Nicoletta Brunelli,1,2 Lorenzo Ricci,1,2 Lucia Florio,1,2 Vincenzo Di Lazzaro1,2 1Unit of Neurology, Neurophysiology, Neurobiology, Department of Medicine, Università Campus Bio-Medico di Roma, Rome, Italy; 2Fondazione Alberto Sordi – Research Institute for Aging, Rome, ItalyAbstract: Neurophysiological and neuroanatomical studies have found that the same basic structural and functional organization of neuronal circuits exists throughout the cortex. This kind of cortical organization, termed canonical circuit, has been functionally demonstrated primarily by studies involving visual striate cortex, and then, the concept has been extended to different cortical areas. In brief, the canonical circuit is composed of superficial pyramidal neurons of layers II/III receiving different inputs and deep pyramidal neurons of layer V that are responsible for cortex output. Superficial and deep pyramidal neurons are reciprocally connected, and inhibitory interneurons participate in modulating the activity of the circuit. The main intuition of this model is that the entire cortical network could be modeled as the repetition of relatively simple modules composed of relatively few types of excitatory and inhibitory, highly interconnected neurons. We will review the origin and the application of the canonical cortical circuit model in the six sections of this paper. The first section (The origins of the concept of canonical circuit: the cat visual cortex reviews the experiments performed in the cat visual cortex, from the origin of the concept of canonical circuit to the most recent developments in the modelization of cortex. The second (The canonical circuit in neocortex and third (Toward a canonical circuit in agranular cortex sections try to extend the concept of canonical circuit to other cortical areas, providing some significant examples of circuit functioning in different cytoarchitectonic
A canonical representation for aggregated Markov processes
Larget, Bret
1998-01-01
A deterministic function of a Markov process is called an aggregated Markov process. We give necessary and sufficient conditions for the equivalence of continuous-time aggregated Markov processes. For both discrete- and continuous-time, we show that any aggregated Markov process which satisfies mild regularity conditions can be directly converted to a canonical representation which is unique for each class of equivalent models, and furthermore, is a minimal parameterization ...
The canon as text for a biblical theology
Directory of Open Access Journals (Sweden)
James A. Loader
2005-10-01
Full Text Available The novelty of the canonical approach is questioned and its fascination at least partly traced to the Reformation, as well as to the post-Reformation’s need for a clear and authoritative canon to perform the function previously performed by the church. This does not minimise the elusiveness and deeply contradictory positions both within the canon and triggered by it. On the one hand, the canon itself is a centripetal phenomenon and does play an important role in exegesis and theology. Even so, on the other hand, it not only contains many difficulties, but also causes various additional problems of a formal as well as a theological nature. The question is mooted whether the canonical approach alleviates or aggravates the dilemma. Since this approach has become a major factor in Christian theology, aspects of the Christian canon are used to gauge whether “canon” is an appropriate category for eliminating difficulties that arise by virtue of its own existence. Problematic uses and appropriations of several Old Testament canons are advanced, as well as evidence in the New Testament of a consciousness that the “old” has been surpassed(“Überbietungsbewußtsein”. It is maintained that at least the Childs version of the canonical approach fails to smooth out these and similar difficulties. As a method it can cater for the New Testament’s (superior role as the hermeneutical standard for evaluating the Old, but flounders on its inability to create the theological unity it claims can solve religious problems exposed by Old Testament historical criticism. It is concluded that canon as a category cannot be dispensed with, but is useful for the opposite of the purpose to which it is conventionally put: far from bringing about theological “unity” or producing a standard for “correct” exegesis, it requires different readings of different canons.
Papike, J. J.; Le, L.; Burger, P. V.; Shearer, C. K.; Bell, A. S.; Jones, J.
2013-01-01
Our research on valence state partitioning began in 2005 with a review of Cr, Fe, Ti, and V partitioning among crystallographic sites in olivine, pyroxene, and spinel [1]. That paper was followed by several on QUE94201 melt composition and specifically on Cr, V, and Eu partitioning between pyroxene and melt [2-5]. This paper represents the continuation of our examination of the partitioning of multivalent V between olivine, spinel, and melt in martian olivine-phyric basalts of Y980459 composition [6, 7]. Here we introduce a new, potentially powerful oxybarometer, V partitioning between spinel and olivine, which can be used when no melt is preserved in the meteorite. The bulk composition of QUE94201 was ideal for our study of martian pyroxene-phyric basalts and specifically the partitioning between pyroxene-melt for Cr, V, and Eu. Likewise, bulk composition Y980459 is ideal for the study of martian olivine-phyric basalts and specifically for olivine-melt, spinel-melt, and spinel-olivine partitioning of V as a function of oxygen fugacity.
Critical adsorption and critical Casimir forces in the canonical ensemble
Gross, Markus; Vasilyev, Oleg; Gambassi, Andrea; Dietrich, S.
2016-08-01
Critical properties of a liquid film between two planar walls are investigated in the canonical ensemble, within which the total number of fluid particles, rather than their chemical potential, is kept constant. The effect of this constraint is analyzed within mean-field theory (MFT) based on a Ginzburg-Landau free-energy functional as well as via Monte Carlo simulations of the three-dimensional Ising model with fixed total magnetization. Within MFT and for finite adsorption strengths at the walls, the thermodynamic properties of the film in the canonical ensemble can be mapped exactly onto a grand canonical ensemble in which the corresponding chemical potential plays the role of the Lagrange multiplier associated with the constraint. However, due to a nonintegrable divergence of the mean-field order parameter profile near a wall, the limit of infinitely strong adsorption turns out to be not well-defined within MFT, because it would necessarily violate the constraint. The critical Casimir force (CCF) acting on the two planar walls of the film is generally found to behave differently in the canonical and grand canonical ensembles. For instance, the canonical CCF in the presence of equal preferential adsorption at the two walls is found to have the opposite sign and a slower decay behavior as a function of the film thickness compared to its grand canonical counterpart. We derive the stress tensor in the canonical ensemble and find that it has the same expression as in the grand canonical case, but with the chemical potential playing the role of the Lagrange multiplier associated with the constraint. The different behavior of the CCF in the two ensembles is rationalized within MFT by showing that, for a prescribed value of the thermodynamic control parameter of the film, i.e., density or chemical potential, the film pressures are identical in the two ensembles, while the corresponding bulk pressures are not.
Canonical Approaches to Applications of the Virial Theorem.
Walton, Jay R; Rivera-Rivera, Luis A; Lucchese, Robert R; Bevan, John W
2016-02-11
Canonical approaches are applied for investigation of the extraordinarily accurate electronic ground state potentials of H2(+), H2, HeH(+), and LiH using the virial theorem. These approaches will be dependent on previous investigations involving the canonical nature of E(R), the Born-Oppenheimer potential, and F(R), the associated force of E(R), that have been demonstrated to be individually canonical to high accuracy in the case of the systems investigated. Now, the canonical nature of the remaining functions in the virial theorem [the electronic kinetic energy T(R), the electrostatic potential energy V(R), and the function W(R) = RF(R)] are investigated and applied to H2, HeH(+), and LiH with H2(+) chosen as reference. The results will be discussed in the context of a different perspective of molecular bonding that goes beyond previous direct applications of the virial theorem. PMID:26788937
Integration of transient receptor potential canonical channels with lipids
Beech, D. J.
2012-01-01
Transient receptor potential canonical (TRPC) channels are the canonical (C) subset of the TRP proteins, which are widely expressed in mammalian cells. They are thought to be primarily involved in determining calcium and sodium entry and have wide-ranging functions that include regulation of cell proliferation, motility and contraction. The channels are modulated by a multiplicity of factors, putatively existing as integrators in the plasma membrane. This review considers the sensitivities of...
Life-cycle assessment of lightweight textile membrane partition walls
Neiva, Sara Daniela Oliveira; Mateus, Ricardo; Macieira, Mónica; Mendonça, Paulo, ed. lit.; Bragança, L.
2012-01-01
This paper analyze the environmental, functional and economical performances of some conceptual lightweights textiles membranes partitions walls and to compare one of them with two technologies present in Portuguese market: i) the heavyweight conventional hollow brick partition wall; and ii) the lightweight reference plasterboard partition wall. Advantages of use textile/ fibrous/ membrane based materials in partition walls are focused and they may contribute for the development of new partit...
kunz, Milan
2006-01-01
Ferrers graphs and tables of partitions are treated as vectors. Matrix operations are used for simple proofs of identities concerning partitions. Interpreting partitions as vectors gives a possibility to generalize partitions on negative numbers. Partitions are then tabulated into lattices and some properties of these lattices are studied. There appears a new identity counting Ferrers graphs packed consecutively into isoscele form. The lattices form the base for tabulating combinatorial ident...
The partitioning of iodides into steam
International Nuclear Information System (INIS)
In order to estimate the likely releases of radioactive iodine during steam generator tube rupture (SGTR) faults, it is necessary to know the relevant partition coefficients as a function of temperature and solution composition. It has been suggested previously that, under SGTR fault conditions, partitioning of free or ion-paired I- into the steam may be more extensive than that for molecular HI. This report uses available information on the partitioning of iodides and other salts to provide a means of estimating the partition coefficient of the iodide ion as a function of boric acid concentration and temperature. (author)
Institute of Scientific and Technical Information of China (English)
LIU Hong-Xia; WANG Zun-Yao; ZHAI Zhi-Cai; LIU Hong-Yan; WANG Lian-Sheng
2007-01-01
Optimized calculation of 35 dialkyl phenyl phosphate compounds (OPs) was carried out at the B3LYP/6-31G* level in Gaussian 98 program. Based on the theoretical linear solvation energy relationship (TLSER) model, the obtained parameters were taken as theoretical descriptors to establish the novel QSPR model for predicting n-octanol/water partition coefficients (IgKow) of OPs. The new model achieved in this work contains three variables, i.e., molecular volume (Vm),dipole moment of the molecules (μ) and enthalpy (H0). For this model, R2 = 0.9167 and SD = 0.31 at large t values. In addition, the variation inflation factors (VIF) of variables are all close to 1.0,suggesting high accuracy of the predicting model. And the results of cross-validation test (q2 =0.8993) and method validation also showed the model of this study exhibited optimum stability and better predictive power than that from semi-empirical method. The model achieved can be used to predict lgKow of congeneric compounds.
Periodicity, the Canon and Sport
Directory of Open Access Journals (Sweden)
Thomas F. Scanlon
2015-10-01
Full Text Available The topic according to this title is admittedly a broad one, embracing two very general concepts of time and of the cultural valuation of artistic products. Both phenomena are, in the present view, largely constructed by their contemporary cultures, and given authority to a great extent from the prestige of the past. The antiquity of tradition brings with it a certain cachet. Even though there may be peripheral debates in any given society which question the specifics of periodization or canonicity, individuals generally accept the consensus designation of a sequence of historical periods and they accept a list of highly valued artistic works as canonical or authoritative. We will first examine some of the processes of periodization and of canon-formation, after which we will discuss some specific examples of how these processes have worked in the sport of two ancient cultures, namely Greece and Mesoamerica.
Variation on a theme of Nathan Fine. New weighted partition identities
Berkovich, Alexander; Uncu, Ali Kemal
2016-01-01
We utilize false theta function results of Nathan Fine to discover two new partition identities involving weights. These relations connect G\\"ollnitz--Gordon type partitions and partitions with distinct odd parts, and partitions into distinct parts and ordinary partitions, respectively. Some of our weights involve a new partition statistic, defined as the number of odd parts of a partition bigger than a given value. Dedicated to our friend, Krishna Alladi, on his 60th birthday.
International Nuclear Information System (INIS)
The grand partition function Z (α,β) of a quantum system is studied, using diagrammatic representations of the perturbation expansion. For a fermions system, it is possible to show, by proper resummation, without approximations but under some 'regularity hypothesis', that Log Z (α,β) takes a form where, besides trivial dependences, α and β only appear through a statistical factor Fk- = [1 + e-α+βεk0-βWk]-1. Wk is a (real) self-consistent potential, generalized to all orders and can be defined by a stationary condition on Log Z (α,β) under variations of Fk-. The thermodynamical quantities take a form analogous to the expressions Landau introduced for the Fermi liquids. The zero temperature limit (for isotropic systems) gives back Goldstone expressions for the ground state of a system. (author)
Partitioning Uncertain Workflows
Huberman, Bernardo A
2015-01-01
It is common practice to partition complex workflows into separate channels in order to speed up their completion times. When this is done within a distributed environment, unavoidable fluctuations make individual realizations depart from the expected average gains. We present a method for breaking any complex workflow into several workloads in such a way that once their outputs are joined, their full completion takes less time and exhibit smaller variance than when running in only one channel. We demonstrate the effectiveness of this method in two different scenarios; the optimization of a convex function and the transmission of a large computer file over the Internet.
Existence of log canonical closures
Hacon, Christopher D
2011-01-01
Let $f:X\\to U$ be a projective morphism of normal varieties and $(X,\\Delta)$ a dlt pair. We prove that if there is an open set $U^0\\subset U$, such that $(X,\\Delta)\\times_U U^0$ has a good minimal model over $U^0$ and the images of all the non-klt centers intersect $U^0$, then $(X,\\Delta)$ has a good minimal model over $U$. As consequences we show the existence of log canonical compactifications for open log canonical pairs, and the fact that the moduli functor of stable schemes satisfies the valuative criterion for properness.
Gauge Theory by canonical Transformations
Koenigstein, Adrian; Stoecker, Horst; Struckmeier, Juergen; Vasak, David; Hanauske, Matthias
2016-01-01
Electromagnetism, the strong and the weak interaction are commonly formulated as gauge theories in a Lagrangian description. In this paper we present an alternative formal derivation of U(1)-gauge theory in a manifestly covariant Hamilton formalism. We make use of canonical transformations as our guiding tool to formalize the gauging procedure. The introduction of the gauge field, its transformation behaviour and a dynamical gauge field Lagrangian/Hamiltonian are unavoidable consequences of this formalism, whereas the form of the free gauge Lagrangian/Hamiltonian depends on the selection of the gauge dependence of the canonically conjugate gauge fields.
Case studies in canonical stewardship.
Cafardi, N P; Hite, J
1985-11-01
In facing the challenges that confront Catholic health care today, it is important to know which civil law forms will assist in preserving the Church's ministry. The proper meshing of civil law and canon law thus provides a vehicle to strengthen the apostolate's work. The case studies presented here suggest several means of applying the principles in the new Code of Canon Law to three potentially problematic situations: the merger of a Catholic and non-Catholic hospital, the leasing of a Catholic hospital to an operating company, and the use of the multicorporate format. PMID:10274590
On admissible canonical mechanics
International Nuclear Information System (INIS)
General solution has been derived for the functional c-number equation which determines all admissible realisations of various mechanics with associative (but not necessary realizable by operators) law of multiplication of the observables. The general solution includes the algebras of observables for the classical and for the quantum mechanics. In addition, the solution includes one new algebra which corresponds formally to purely imaginary value to the Planck constant. The mathematical difficulties of treating the new algebra are discussed
Resistant multiple sparse canonical correlation.
Coleman, Jacob; Replogle, Joseph; Chandler, Gabriel; Hardin, Johanna
2016-04-01
Canonical correlation analysis (CCA) is a multivariate technique that takes two datasets and forms the most highly correlated possible pairs of linear combinations between them. Each subsequent pair of linear combinations is orthogonal to the preceding pair, meaning that new information is gleaned from each pair. By looking at the magnitude of coefficient values, we can find out which variables can be grouped together, thus better understanding multiple interactions that are otherwise difficult to compute or grasp intuitively. CCA appears to have quite powerful applications to high-throughput data, as we can use it to discover, for example, relationships between gene expression and gene copy number variation. One of the biggest problems of CCA is that the number of variables (often upwards of 10,000) makes biological interpretation of linear combinations nearly impossible. To limit variable output, we have employed a method known as sparse canonical correlation analysis (SCCA), while adding estimation which is resistant to extreme observations or other types of deviant data. In this paper, we have demonstrated the success of resistant estimation in variable selection using SCCA. Additionally, we have used SCCA to find multiple canonical pairs for extended knowledge about the datasets at hand. Again, using resistant estimators provided more accurate estimates than standard estimators in the multiple canonical correlation setting. R code is available and documented at https://github.com/hardin47/rmscca. PMID:26963062
Romanticism, Sexuality, and the Canon.
Rowe, Kathleen K.
1990-01-01
Traces the Romanticism in the work and persona of film director Jean-Luc Godard. Examines the contradictions posed by Godard's politics and representations of sexuality. Asserts, that by bringing an ironic distance to the works of such canonized directors, viewers can take pleasure in those works despite their contradictions. (MM)
Classification algorithms using adaptive partitioning
Binev, Peter
2014-12-01
© 2014 Institute of Mathematical Statistics. Algorithms for binary classification based on adaptive tree partitioning are formulated and analyzed for both their risk performance and their friendliness to numerical implementation. The algorithms can be viewed as generating a set approximation to the Bayes set and thus fall into the general category of set estimators. In contrast with the most studied tree-based algorithms, which utilize piecewise constant approximation on the generated partition [IEEE Trans. Inform. Theory 52 (2006) 1335.1353; Mach. Learn. 66 (2007) 209.242], we consider decorated trees, which allow us to derive higher order methods. Convergence rates for these methods are derived in terms the parameter - of margin conditions and a rate s of best approximation of the Bayes set by decorated adaptive partitions. They can also be expressed in terms of the Besov smoothness β of the regression function that governs its approximability by piecewise polynomials on adaptive partition. The execution of the algorithms does not require knowledge of the smoothness or margin conditions. Besov smoothness conditions are weaker than the commonly used Holder conditions, which govern approximation by nonadaptive partitions, and therefore for a given regression function can result in a higher rate of convergence. This in turn mitigates the compatibility conflict between smoothness and margin parameters.
Canonical Notch activation in osteocytes causes osteopetrosis.
Canalis, Ernesto; Bridgewater, David; Schilling, Lauren; Zanotti, Stefano
2016-01-15
Activation of Notch1 in cells of the osteoblastic lineage inhibits osteoblast differentiation/function and causes osteopenia, whereas its activation in osteocytes causes a distinct osteopetrotic phenotype. To explore mechanisms responsible, we established the contributions of canonical Notch signaling (Rbpjκ dependent) to osteocyte function. Transgenics expressing Cre recombinase under the control of the dentin matrix protein-1 (Dmp1) promoter were crossed with Rbpjκ conditional mice to generate Dmp1-Cre(+/-);Rbpjκ(Δ/Δ) mice. These mice did not have a skeletal phenotype, indicating that Rbpjκ is dispensable for osteocyte function. To study the Rbpjκ contribution to Notch activation, Rosa(Notch) mice, where a loxP-flanked STOP cassette is placed between the Rosa26 promoter and the NICD coding sequence, were crossed with Dmp1-Cre transgenic mice and studied in the context (Dmp1-Cre(+/-);Rosa(Notch);Rbpjκ(Δ/Δ)) or not (Dmp1-Cre(+/-);Rosa(Notch)) of Rbpjκ inactivation. Dmp1-Cre(+/-);Rosa(Notch) mice exhibited increased femoral trabecular bone volume and decreased osteoclasts and bone resorption. The phenotype was reversed in the context of the Rbpjκ inactivation, demonstrating that Notch canonical signaling was accountable for the phenotype. Notch activation downregulated Sost and Dkk1 and upregulated Axin2, Tnfrsf11b, and Tnfsf11 mRNA expression, and these effects were not observed in the context of the Rbpjκ inactivation. In conclusion, Notch activation in osteocytes suppresses bone resorption and increases bone volume by utilization of canonical signals that also result in the inhibition of Sost and Dkk1 and upregulation of Wnt signaling. PMID:26578715
Canonical particle tracking in undulator fields
International Nuclear Information System (INIS)
A new algebraic mapping routine for particle tracking across wiggler and undulator fields in presented. It is based on a power series expansion of the generating function to guarantee fully canonical transformations. This method is 10 to 100 times faster than integration routines, applied in tracking codes like BETA or RACETRACK. The tracking method presented is not restricted to wigglers and undulators, it can be applied to other magnetic fields as well such as fringing fields of quadrupoles or dipoles if the suggested expansion converges
Basic Canonical Brackets Without Canonical Conjugate Momenta: Supersymmetric Harmonic Oscillator
Shukla, A; Malik, R P
2014-01-01
We exploit the ideas of spin-statistics theorem, normal-ordering and the key concepts behind the symmetry principles to derive the canonical (anti)commutators for the case of a one (0 + 1)-dimensional (1D) supersymmetric (SUSY) harmonic oscillator without taking the help of the mathematical definition of the canonical conjugate momenta with respect to the bosonic and fermionic variables of this toy model for the Hodge theory (where the continuous and discrete symmetries of the theory provide the physical realizations of the de Rham cohomological operators of differential geometry). In our present endeavor, it is the full set of continuous symmetries and their corresponding generators that lead to the derivation of basic (anti)commutators amongst the creation and annihilation operators that appear in the normal mode expansions of the dynamical variables of our theory.
Canonical and non-canonical pathways of osteoclast formation
Knowles, H.J.; Athanasou, N A
2009-01-01
Physiological and pathological bone resorption is mediated by osteoclasts, multinucleated cells which are formed by the fusion of monocyte / macrophage precursors. The canonical pathway of osteoclast formation requires the presence of the receptor activator for NFkB ligand (RANKL) and macrophage colony stimulating factor (M-CSF). Noncanonical pathways of osteoclast formation have been described in which cytokines / growth factors can substitute for RANKL or M-CSF to...
Czech Academy of Sciences Publication Activity Database
Le Bagousse-Pinguet, Y.; de Bello, Francesco; Vandewalle, M.; Lepš, J.; Sykes, M. T.
2014-01-01
Roč. 102, č. 2 (2014), s. 466-474. ISSN 0022-0477 R&D Projects: GA ČR GAP505/12/1296 Institutional support: RVO:67985939 Keywords : functional diversity * species richness * trait overlap Subject RIV: EH - Ecology, Behaviour Impact factor: 5.521, year: 2014
International Nuclear Information System (INIS)
To explore local structures around lithium ions and to estimate lithium isotopic reduced partition function ratios (RPFRs) of solvated lithium ions in ethylene carbonate (EC), methylethyl carbonate (MEC) and EC/MEC mixed solvent systems, ab initio molecular orbital calculations at the HF/6-31G(d) level of theory were carried out. Both EC and MEC were coordinated to lithium ions using their carboxyl oxygens and the Li-O bond distance increase with increasing solvation number up to 4 in the primary solvation sphere both in EC and MEC systems. Binding energy calculations suggested that EC was preferentially coordinated to the lithium ion in the EC/MEC mixed solvent system. RPFRs of solvated lithium ions were convex functions of the solvation number between 1 and 4 and took the maxima at 3 both in EC and MEC systems. The RPFR value in EC/MEC mixed solvent system was estimated to be 1.07818 at 25degC. (author)
Canonical proper time quantum gravitation
Lindesay, James
2015-05-01
At the root of the tensions involved in modeling the quantum dynamics of gravitating systems are the subtleties of quantum locality. Quantum mechanics describes physical phenomena using a theory of non-local phase relationships (non-local in the sense that quantum states maintain a space-like coherence that is acausal). However, the principle of equivalence in general relativity asserts that freely falling frames are locally inertial frames of reference. Thus, gravitating systems are often described using constituents that are freely falling, undergoing geodesic motion defining well localized trajectories. The canonical proper time formulation of relativistic dynamics is particularly useful for describing such inertial constituents using the coordinates of non-inertial observers. The physics of the simplest of gravitating inertial quantum systems, consistent with presented experimental evidence, will be examined. Subsequently, descriptions of both weakly and strongly gravitating quantum systems will be developed using canonical proper gravitation.
Canonical computations of cerebral cortex.
Miller, Kenneth D
2016-04-01
The idea that there is a fundamental cortical circuit that performs canonical computations remains compelling though far from proven. Here we review evidence for two canonical operations within sensory cortical areas: a feedforward computation of selectivity; and a recurrent computation of gain in which, given sufficiently strong external input, perhaps from multiple sources, intracortical input largely, but not completely, cancels this external input. This operation leads to many characteristic cortical nonlinearities in integrating multiple stimuli. The cortical computation must combine such local processing with hierarchical processing across areas. We point to important changes in moving from sensory cortex to motor and frontal cortex and the possibility of substantial differences between cortex in rodents vs. species with columnar organization of selectivity. PMID:26868041
Three Dimensional Canonical Quantum Gravity
Matschull, Hans-Juergen
1995-01-01
General aspects of vielbein representation, ADM formulation and canonical quantization of gravity are reviewed using pure gravity in three dimensions as a toy model. The classical part focusses on the role of observers in general relativity, which will later be identified with quantum observers. A precise definition of gauge symmetries and a classification of inequivalent solutions of Einstein's equations in dreibein formalism is given as well. In the quantum part the construction of the phys...
Resistant Multiple Sparse Canonical Correlation
Coleman, Jacob; Replogle, Joseph; Chandler, Gabriel; Hardin, Johanna
2014-01-01
Canonical Correlation Analysis (CCA) is a multivariate technique that takes two datasets and forms the most highly correlated possible pairs of linear combinations between them. Each subsequent pair of linear combinations is orthogonal to the preceding pair, meaning that new information is gleaned from each pair. By looking at the magnitude of coefficient values, we can find out which variables can be grouped together, thus better understanding multiple interactions that are otherwise difficu...
S Natarajan; Chakraborty, S.; M. Ganapathi; Subramaniam, M
2013-01-01
In this paper, the effect of local defects, viz., cracks and cutouts on the buckling behaviour of functionally graded material plates subjected to mechanical and thermal load is numerically studied. The internal discontinuities, viz., cracks and cutouts are represented independent of the mesh within the framework of the extended finite element method and an enriched shear flexible 4-noded quadrilateral element is used for the spatial discretization. The properties are assumed to vary only in ...
Fox, R. J.; Bellwood, D. R.
2013-03-01
Niche theory predicts that coexisting species minimise competition by evolving morphological or behavioural specialisations that allow them to spread out along resource axes such as space, diet and temporal activity. These specialisations define how a species interacts with its environment and, by extension, determine its functional role. Here, we examine the feeding niche of three species of coral reef-dwelling rabbitfishes (Siganidae, Siganus). By comparing aspects of their feeding behaviour (bite location, bite rate, foraging distance) with that of representative species from two other abundant herbivorous fish families, the parrotfishes (Labridae, Scarus) and surgeonfishes (Acanthuridae, Acanthurus), we examine whether rabbitfishes have a feeding niche distinct from other members of the herbivore guild. Measurements of the penetration of the fishes' snouts and bodies into reef concavities when feeding revealed that rabbitfish fed to a greater degree from reef crevices and interstices than other herbivores. There was just a 40 % overlap in the penetration-depth niche between rabbitfish and surgeonfish and a 45 % overlap between rabbitfish and parrotfish, compared with the almost complete niche overlap (95 %) recorded for parrotfish and surgeonfish along this spatial niche axis. Aspects of the morphology of rabbitfish which may contribute to this niche segregation include a comparatively longer, narrower snout and narrower head. Our results suggest that sympatric coexistence of rabbitfish and other reef herbivores is facilitated by segregation along a spatial (and potentially dietary) axis. This segregation results in a unique functional role for rabbitfishes among roving herbivores that of "crevice-browser": a group that specifically feeds on crevice-dwelling algal or benthic organisms. This functional trait may have implications for reef ecosystem processes in terms of controlling the successional development of crevice-based algal communities, reducing their
International Nuclear Information System (INIS)
We reformulate the Bekenstein bound as the requirement of positivity of the Helmholtz free energy at the minimum value of the function L=E-S/(2πR), where R is some measure of the size of the system. The minimum of L occurs at the temperature T=1/(2πR). In the case of n-dimensional anti-de Sitter spacetime, the rather poorly defined size R acquires a precise definition in terms of the AdS radius l, with R=l/(n-2). We previously found that the Bekenstein bound holds for all known black holes in AdS. However, in this paper we show that the Bekenstein bound is not generally valid for free quantum fields in AdS, even if one includes the Casimir energy. Some other aspects of thermodynamics in anti-de Sitter spacetime are briefly touched upon
International Nuclear Information System (INIS)
With the final goal to elucidate boron isotope fractionation observed experimentally, molecular orbital calculations were performed on boric acid and borate monomers and dimers. The geometries of B(OH)3 and B(OH)4- were first optimized and their vibrational frequencies were calculated at their optimized structures. The estimated 11B-to-10B isotopic reduced partition function ratios (RPFRs) of B(OH)3 and B(OH)4- and the calculated equilibrium constant of the boron isotope exchange reaction between the two boron species revealed that a more advanced molecular orbital theory with a higher level basis set did not necessarily yield better results. It was concluded that HF/6-31G(d) calculations were most appropriate for the present purpose. The RPFRs of the dimers, H4B2O5, H5B2O6- and H6B2O72-, estimated from the RPFRs of the monomers by the use of additivity of the logarithm of RPFRs agreed with those calculated using the frequencies of the dimers within a margin of 1%. This error corresponded to the error of 5% on ln (RPFR). The equilibrium constant of boron isotope exchange reaction between two boron species among the monomer and dimers at 25degC varied from 1.0207 to 1.0360, indicating the importance of accurate estimation of the RPFRs of polyboric acids and polyborates in real systems. (author)
Izmaĭlov, T R; Pan'shin, G A; Datsenko, P V
2012-01-01
The treatment results of 396 patients with morphologically verified grade 3-4 malignant brain tumors receiving conventional irradiation regimen and irradiation by medium-sized fractions were analyzed to form institutional guidelines.The standard mode of fractionation with a single dose of 2 Gy and total focal dose (TFD) of 60 Gy is appropriate for patients with initial Karnofsky status of 60-100% and Recursive Partition Analysis (RPA) class I-III. TFD increase to 60-62 Gy in grade 4 gliomas and 54-56 Gy in grade 3 gliomas grants a significant improve in overall survival. An increase of a single irradiation fraction to 3 Gy may be used for patients with initially low functional status (Karnofsky 30-50%) and RPA classes IV-VI. In these cases it is advisable to use the TFD of 45 Gy or more (TFD of equivalent regimen with a dose greater than 54 Gy). The mentioned fractionation regimens could be recommended for the use in clinical practice to improve the results of high-grade gliomas treatment. PMID:22888653
Delaney, J. S.; Sutton, S. R.; Newville, M.; Jones, J. H.; Hanson, B.; Dyar, M. D.; Schreiber, H.
2000-01-01
Oxidation state microanalyses for V in glass have been made by calibrating XANES spectral features with optical spectroscopic measurements. The oxidation state change with fugacity of O2 will strongly influence partitioning results.
General relativity as an extended canonical gauge theory
Struckmeier, J.
2015-04-01
It is widely accepted that the fundamental geometrical law of nature should follow from an action principle. The particular subset of transformations of a system's dynamical variables that maintain the form of the action principle comprises the group of canonical transformations. In the context of canonical field theory, the adjective "extended" signifies that not only the fields but also the space-time geometry is subject to transformation. Thus, in order to be physical, the transition to another, possibly noninertial frame of reference must necessarily constitute an extended canonical transformation that defines the general mapping of the connection coefficients, hence the quantities that determine the space-time curvature and torsion of the respective reference frame. The canonical transformation formalism defines simultaneously the transformation rules for the conjugates of the connection coefficients and for the Hamiltonian. As will be shown, this yields unambiguously a particular Hamiltonian that is form-invariant under the canonical transformation of the connection coefficients and thus satisfies the general principle of relativity. This Hamiltonian turns out to be a quadratic function of the curvature tensor. Its Legendre-transformed counterpart then establishes a unique Lagrangian description of the dynamics of space-time that is not postulated but derived from basic principles, namely the action principle and the general principle of relativity. Moreover, the resulting theory satisfies the principle of scale invariance and is renormalizable.
Institute of Scientific and Technical Information of China (English)
范志浩; 姜灿荣
2012-01-01
根据西藏的自然环境条件，结合林地保护管理现状，将全区林地划分为4个功能区，并就各区域林地的功能定位、差别化保护利用以及相应的管理措施进行探讨。%According to the natural environment, combining with forest land protection and management situa- tion ,Tibet was classified as four forest lands functional partition. In this paper, it discussed forest land function orientation, discrepant protection and utilization and appropriate management measures for each forest lands functional partition
Regenerative partition structures
Gnedin, Alexander; Pitman, Jim
2004-01-01
We consider Kingman's partition structures which are regenerative with respect to a general operation of random deletion of some part. Prototypes of this class are the Ewens partition structures which Kingman characterised by regeneration after deletion of a part chosen by size-biased sampling. We associate each regenerative partition structure with a corresponding regenerative composition structure, which (as we showed in a previous paper) can be associated in turn with a regenerative random...
Alorizi, Seyed Morteza Emami; Nimruzi, Majid
2016-01-01
Background: Stroke has a huge negative impact on the society and more adversely affect women. There is scarce evidence about any neuroprotective effects of commonly used drug in acute stroke. Bushnell et al. provided a guideline focusing on the risk factors of stroke unique to women, including reproductive factors, metabolic syndrome, obesity, atrial fibrillation, and migraine with aura. The ten variables cited by Avicenna in Canon of Medicine would compensate for the gaps mentioned in this guideline. The prescribed drugs should be selected qualitatively opposite to Mizaj (warm-cold and wet-dry qualities induced by disease state) of the disease and according to ten variables, including the nature of the affected organ, intensity of disease, sex, age, habit, season, place of living, occupation, stamina and physical status. Methods: Information related to stroke was searched in Canon of Medicine, which is an outstanding book in traditional Persian medicine written by Avicenna. Results: A hemorrhagic stroke is the result of increasing sanguine humor in the body. Sanguine has warm-wet quality, and should be treated with food and drugs that quench the abundance of blood in the body. An acute episode of ischemic stroke is due to the abundance of phlegm that causes a blockage in the cerebral vessels. Phlegm has cold-wet quality and treatment should be started with compound medicines that either solve the phlegm or eject it from the body. Conclusion: Avicenna has cited in Canon of Medicine that women have cold and wet temperament compared to men. For this reason, they are more prone to accumulation of phlegm in their body organs including the liver, joints and vessels, and consequently in the risk of fatty liver, degenerative joint disease, atherosclerosis, and stroke especially the ischemic one. This is in accordance with epidemiological studies that showed higher rate of ischemic stroke in women rather than hemorrhagic one. PMID:26722147
Dibaryons as canonically quantized biskyrmions
Krupovnickas, T; Riska, D O
2000-01-01
The characteristic feature of the ground state configuration of the Skyrme model description of nuclei is the absence of recognizable individual nucleons. The ground state of the skyrmion with baryon number 2 is axially symmetric, and is well approximated by a simple rational map, which represents a direct generalization of Skyrme's hedgehog ansatz for the nucleon. If the Lagrangian density is canonically quantized this configuration may support excitations that lie close and possible below the threshold for pion decay, and therefore describe dibaryons. The quantum corrections stabilize these solutions, the mass density of which have the correct exponential fall off at large distances.
Canonical metrics on complex manifold
Institute of Scientific and Technical Information of China (English)
YAU Shing-Tung
2008-01-01
@@ Complex manifolds are topological spaces that are covered by coordinate charts where the Coordinate changes are given by holomorphic transformations. For example, Riemann surfaces are one dimensional complex manifolds. In order to understand complex manifolds, it is useful to introduce metrics that are compatible with the complex structure. In general, we should have a pair (M, ds2M) where ds2M is the metric. The metric is said to be canonical if any biholomorphisms of the complex manifolds are automatically isometries. Such metrics can naturally be used to describe invariants of the complex structures of the manifold.
Canonical metrics on complex manifold
Institute of Scientific and Technical Information of China (English)
YAU; Shing-Tung(Yau; S.-T.)
2008-01-01
Complex manifolds are topological spaces that are covered by coordinate charts where the coordinate changes are given by holomorphic transformations.For example,Riemann surfaces are one dimensional complex manifolds.In order to understand complex manifolds,it is useful to introduce metrics that are compatible with the complex structure.In general,we should have a pair(M,ds~2_M)where ds~2_M is the metric.The metric is said to be canonical if any biholomorphisms of the complex manifolds are automatically isometries.Such metrics can naturally be used to describe invariants of the complex structures of the manifold.
Gauge fixing and canonical quantization
International Nuclear Information System (INIS)
We study the canonical quantization of non-Abelian gauge fields in the temporal gauge A0 = 0. We impose the constraint condition of Gauss's law by performing a point transformation into any of a large class of noncovariant gauges. The Faddeev and Popov operator arises naturally in this procedure; indeed, we prove the equivalence of all gauges in this class. We discuss the nonexistence of some simple gauges and show how topological considerations reduce the theory to quantum mechanics on an infinite-dimensional periodic hypersurface
DEFF Research Database (Denmark)
Sloth, Peter
1990-01-01
Density profiles and partition coefficients are obtained for hard-sphere fluids inside hard, spherical pores of different sizes by grand canonical ensemble Monte Carlo calculations. The Monte Carlo results are compared to the results obtained by application of different kinds of integral equation...
Canonical path integral quantization of Einstein's gravitational field
Muslih, Sami I.
2000-01-01
The connection between the canonical and the path integral formulations of Einstein's gravitational field is discussed using the Hamilton - Jacobi method. Unlike conventional methods, it is shown that our path integral method leads to obtain the measure of integration with no $\\delta$- functions, no need to fix any gauge and so no ambiguous deteminants will appear.
The Euler–Riemann gases, and partition identities
International Nuclear Information System (INIS)
The Euler theorem in partition theory and its generalization are derived from a non-interacting quantum field theory in which each bosonic mode with a given frequency is equivalent to a sum of bosonic mode whose frequency is twice (s-times) as much, and a fermionic (parafermionic) mode with the same frequency. Explicit formulas for the graded parafermionic partition functions are obtained, and the inverse of the graded partition function (IGPPF), turns out to be bosonic (fermionic) partition function depending on the parity of the order s of the parafermions. It is also shown that these partition functions are generating functions of partitions of integers with restrictions, the Euler generating function is identified with the inverse of the graded parafermionic partition function of order 2. As a result we obtain new sequences of partitions of integers with given restrictions. If the parity of the order s is even, then mixing a system of parafermions with a system whose partition function is (IGPPF), results in a system of fermions and bosons. On the other hand, if the parity of s is odd, then, the system we obtain is still a mixture of fermions and bosons but the corresponding Fock space of states is truncated. It turns out that these partition functions are given in terms of the Jacobi theta function θ4, and generate sequences in partition theory. Our partition functions coincide with the overpartitions of Corteel and Lovejoy, and jagged partitions in conformal field theory. Also, the partition functions obtained are related to the Ramond characters of the superconformal minimal models, and in the counting of the Moore–Read edge spectra that appear in the fractional quantum Hall effect. The different partition functions for the Riemann gas that are the counter parts of the Euler gas are obtained by a simple change of variables. In particular the counter part of the Jacobi theta function is (ζ(2t))/(ζ(t)2) . Finally, we propose two formulas which brings the
A Canonical Laplacian on the Algebra of Densities on a Projectively Connected Manifold
George, Jacob
2009-01-01
On a manifold with a projective connection we canonically assign a second order differential operator acting on the algebra of all densities to any tensor density $S^{ij}$ of fixed weight $\\lambda$. In particular, this implies that on any projectively connected manifold, a `bracket' (symmetric biderivation) on the algebra of functions extends canonically to the algebra of densities.
Incompatibility boundaries for properties of community partitions
Browet, Arnaud; Sarlette, Alain
2016-01-01
We prove the incompatibility of certain desirable properties of community partition quality functions. Our results generalize the impossibility result of [Kleinberg 2003] by considering sets of weaker properties. In particular, we use an alternative notion to solve the central issue of the consistency property. (The latter means that modifying the graph in a way consistent with a partition should not have counterintuitive effects). Our results clearly show that community partition methods should not be expected to perfectly satisfy all ideally desired properties. We then proceed to show that this incompatibility no longer holds when slightly relaxed versions of the properties are considered, and we provide in fact examples of simple quality functions satisfying these relaxed properties. An experimental study of these quality functions shows a behavior comparable to established methods in some situations, but more debatable results in others. This suggests that defining a notion of good partition in communitie...
Li, Zhendong; Liu, Wenjian
2016-01-01
Complicated mathematical equations involving tensors with permutation symmetries are frequently encountered in fields such as quantum chemistry, e.g., those in coupled cluster theories and derivatives of wavefunction parameters. In automatic derivations of these equations, a key step is the collection of product terms that can be found identical by using permutation symmetries or relabelling dummy indices. In the present work, we define a canonical form for a general tensor product in the presence of permutation symmetries as a result of the classification of all tensor products from a group theoretical point of view. To make such definition of practical use, we provide an efficient algorithm to compute the canonical form by combining the classical backtrack search for permutation groups and the idea of partitions used in graph isomorphism algorithms. The resulted algorithm can compute canonical forms and generators of the automorphism groups of tensor expressions. Moreover, for tensor products with external ...
Controlled levels of canonical Wnt signaling are required for neural crest migration.
Maj, Ewa; Künneke, Lutz; Loresch, Elisabeth; Grund, Anita; Melchert, Juliane; Pieler, Tomas; Aspelmeier, Timo; Borchers, Annette
2016-09-01
Canonical Wnt signaling plays a dominant role in the development of the neural crest (NC), a highly migratory cell population that generates a vast array of cell types. Canonical Wnt signaling is required for NC induction as well as differentiation, however its role in NC migration remains largely unknown. Analyzing nuclear localization of β-catenin as readout for canonical Wnt activity, we detect nuclear β-catenin in premigratory but not migratory Xenopus NC cells suggesting that canonical Wnt activity has to decrease to basal levels to enable NC migration. To define a possible function of canonical Wnt signaling in Xenopus NC migration, canonical Wnt signaling was modulated at different time points after NC induction. This was accomplished using either chemical modulators affecting β-catenin stability or inducible glucocorticoid fusion constructs of Lef/Tcf transcription factors. In vivo analysis of NC migration by whole mount in situ hybridization demonstrates that ectopic activation of canonical Wnt signaling inhibits cranial NC migration. Further, NC transplantation experiments confirm that this effect is tissue-autonomous. In addition, live-cell imaging in combination with biophysical data analysis of explanted NC cells confirms the in vivo findings and demonstrates that modulation of canonical Wnt signaling affects the ability of NC cells to perform single cell migration. Thus, our data support the hypothesis that canonical Wnt signaling needs to be tightly controlled to enable migration of NC cells. PMID:27341758
Spectral zeta function and non-perturbative effects in ABJM Fermi-gas
International Nuclear Information System (INIS)
The exact partition function in ABJM theory on three-sphere can be regarded as a canonical partition function of a non-interacting Fermi-gas with an unconventional Hamiltonian. All the information on the partition function is encoded in the discrete spectrum of this Hamiltonian. We explain how (quantum mechanical) non-perturbative corrections in the Fermi-gas system appear from a spectral consideration. Basic tools in our analysis are a Mellin-Barnes type integral representation and a spectral zeta function. From a consistency with known results, we conjecture that the spectral zeta function in the ABJM Fermi-gas has an infinite number of ''non-perturbative'' poles, which are invisible in the semi-classical expansion of the Planck constant. We observe that these poles indeed appear after summing up perturbative corrections. As a consequence, the perturbative resummation of the spectral zeta function causes non-perturbative corrections to the grand canonical partition function. We also present another example associated with a spectral problem in topological string theory. A conjectured non-perturbative free energy on the resolved conifold is successfully reproduced in this framework.
Spectral zeta function and non-perturbative effects in ABJM Fermi-gas
Hatsuda, Yasuyuki
2015-01-01
The exact partition function in ABJM theory on three-sphere can be regarded as a canonical partition function of a non-interacting Fermi-gas with an unconventional Hamiltonian. All the information on the partition function is encoded in the discrete spectrum of this Hamiltonian. We explain how (quantum mechanical) non-perturbative corrections in the Fermi-gas system appear from a spectral consideration. Basic tools in our analysis are a Mellin-Barnes type integral representation and a spectral zeta function. From a consistency with known results, we conjecture that the spectral zeta function in the ABJM Fermi-gas has an infinite number of "non-perturbative" poles, which are invisible in the semi-classical expansion of the Planck constant. We observe that these poles indeed appear after summing up perturbative corrections. As a consequence, the perturbative resummation of the spectral zeta function causes non-perturbative corrections to the grand canonical partition function. We also present another example as...
Integral canonical models for Spin Shimura varieties
Pera, Keerthi Madapusi
2012-01-01
We construct regular integral canonical models for Shimura varieties attached to Spin groups at (possibly ramified) odd primes. We exhibit these models as schemes of 'relative PEL type' over integral canonical models of larger Spin Shimura varieties with good reduction. Work of Vasiu-Zink then shows that the classical Kuga-Satake construction extends over the integral model and that the integral models we construct are canonical in a very precise sense. We also construct good compactification...
n-Level Hypergraph Partitioning
Henne, Vitali; Meyerhenke, Henning; Sanders, Peter; Schlag, Sebastian; Schulz, Christian
2015-01-01
We develop a multilevel algorithm for hypergraph partitioning that contracts the vertices one at a time and thus allows very high quality. This includes a rating function that avoids nonuniform vertex weights, an efficient "semi-dynamic" hypergraph data structure, a very fast coarsening algorithm, and two new local search algorithms. One is a $k$-way hypergraph adaptation of Fiduccia-Mattheyses local search and gives high quality at reasonable cost. The other is an adaptation of size-constrai...
Canonical curves with low apolarity
Ballico, Edoardo; Notari, Roberto
2010-01-01
Let $k$ be an algebraically closed field and let $C$ be a non--hyperelliptic smooth projective curve of genus $g$ defined over $k$. Since the canonical model of $C$ is arithmetically Gorenstein, Macaulay's theory of inverse systems allows to associate to $C$ a cubic form $f$ in the divided power $k$--algebra $R$ in $g-2$ variables. The apolarity of $C$ is the minimal number $t$ of linear form in $R$ needed to write $f$ as sum of their divided power cubes. It is easy to see that the apolarity of $C$ is at least $g-2$ and P. De Poi and F. Zucconi classified curves with apolarity $g-2$ when $k$ is the complex field. In this paper, we give a complete, characteristic free, classification of curves $C$ with apolarity $g-1$ (and $g-2$).
Directory of Open Access Journals (Sweden)
Karina Beatriz Lemes
2010-11-01
Full Text Available Intentaremos mostrar cómo venimos trabajando con la reconstrucción de la memoria literaria de la provincia de Misiones a partir de la recopilación de los manuscritos de sus autores más representativos. Hemos utilizado para nuestra lectura, en cruce con la crítica genética, las relaciones que Fernando Ainsa establece entre canon y periferia, espacios de la memoria y construcción de la utopía. Ainsa concibe la escritura como proceso genético que en su origen es personal, visceral y solitario, una búsqueda constante de identidad que se enriquece en contacto con el mundo, con la apertura de fronteras. Estas vinculaciones nos han permitido interpretar las prácticas sociales que fundaron actividades estéticas en la distancia de los centros de poder argentinos.This paper shows some findings of our ongoing research project dealing with the recuperation of literary memory in the province of Misiones by analysing a compilation of the literary manuscripts by the most representative authors of this northern region of Argentina. Here, we follow Fernado Ainsa’s notions of canon and periphery, of memory spaces and construction of utopias. Ainsa sees the act of writing as a genetic process for it originates within a personal, visceral, and solitary realm. For Ainsa, writing is also a permanent search for identity which becomes richer when in contact with the world, when frontiers open up. These concepts allow us to interpret the social practices that gave birth to these aesthetic projects far away from Argentina’s power centers.
A single NFκB system for both canonical and non-canonical signaling
Institute of Scientific and Technical Information of China (English)
Vincent Feng-Sheng Shih; Rachel Tsui; Andrew Caldwell; Alexander Hoffmann
2011-01-01
Two distinct nuclear factor κB(NFκB)signaling pathways have been described; the canonical pathway that mediates inflammatory responses,and the non-canonical pathway that is involved in immune cell differentiation and maturation and secondary lymphoid organogenesis.The former is dependent on the IκB kinase adaptor molecule NEMO,the latter is independent of it.Here,we review the molecular mechanisms of regulation in each signaling axis and attempt to relate the apparent regulatory logic to the physiological function.Further,we review the recent evidence for extensive cross-regulation between these two signaling axes and summarize them in a wiring diagram.These observations suggest that NEMO-dependent and-independent signaling should be viewed within the context of a single NFκB signaling system,which mediates signaling from both inflammatory and organogenic stimuli in an integrated manner.As in other regulatory biological systems,a systems approach including mathematical models that include quantitative and kinetic information will be necessary to characterize the network properties that mediate physiological function,and that may break down to cause or contribute to pathology.
Towards a 'canonical' agranular cortical microcircuit
Directory of Open Access Journals (Sweden)
Sarah F. Beul
2015-01-01
Full Text Available Based on regularities in the intrinsic microcircuitry of cortical areas, variants of a 'canonical' cortical microcircuit have been proposed and widely adopted, particularly in computational neuroscience and neuroinformatics. However, this circuit is founded on striate cortex, which manifests perhaps the most extreme instance of cortical organization, in terms of a very high density of cells in highly differentiated cortical layers. Most other cortical regions have a less well differentiated architecture, stretching in gradients from the very dense eulaminate primary cortical areas to the other extreme of dysgranular and agranular areas of low density and poor laminar differentiation. It is unlikely for the patterns of inter- and intra-laminar connections to be uniform in spite of strong variations of their structural substrate. This assumption is corroborated by reports of divergence in intrinsic circuitry across the cortex. Consequently, it remains an important goal to define local microcircuits for a variety of cortical types, in particular, agranular cortical regions. As a counterpoint to the striate microcircuit, which may be anchored in an exceptional cytoarchitecture, we here outline a tentative microcircuit for agranular cortex. The circuit is based on a synthesis of the available literature on the local microcircuitry in agranular cortical areas of the rodent brain, investigated by anatomical and electrophysiological approaches. A central observation of these investigations is a weakening of interlaminar inhibition as cortical cytoarchitecture becomes less distinctive. Thus, our study of agranular microcircuitry revealed deviations from the well-known 'canonical' microcircuit established for striate cortex, suggesting variations in the intrinsic circuitry across the cortex that may be functionally relevant.
Thinning Invariant Partition Structures
Starr, Shannon
2011-01-01
A partition structure is a random point process on $[0,1]$ whose points sum to 1, almost surely. In the case that there are infinitely many points to begin with, we consider a thinning action by: first, removing points independently, such that each point survives with probability $p>0$; and, secondly, rescaling the remaining points by an overall factor to normalize the sum again to 1. We prove that the partition structures which are "thinning divisible" for a sequence of $p$'s converging to 0 are mixtures of the Poisson-Kingman partition structures. We also consider the property of being "thinning invariant" for all $p \\in (0,1)$.
CANONICAL EXTENSIONS OF SYMMETRIC LINEAR RELATIONS
Sandovici, Adrian; Davidson, KR; Gaspar, D; Stratila, S; Timotin, D; Vasilescu, FH
2006-01-01
The concept of canonical extension of Hermitian operators has been recently introduced by A. Kuzhel. This paper deals with a generalization of this notion to the case of symmetric linear relations. Namely, canonical regular extensions of symmetric linear relations in Hilbert spaces are studied. The
2010-07-01
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2010-07-01
... Responsibility § 10.83 Canon 7. A practitioner should represent a client zealously within the bounds of the law. ... 37 Patents, Trademarks, and Copyrights 1 2010-07-01 2010-07-01 false Canon 7. 10.83 Section 10.83 Patents, Trademarks, and Copyrights UNITED STATES PATENT AND TRADEMARK OFFICE, DEPARTMENT OF...
Extending canonical Monte Carlo methods: II
International Nuclear Information System (INIS)
We have previously presented a methodology for extending canonical Monte Carlo methods inspired by a suitable extension of the canonical fluctuation relation C = β2(δE2) compatible with negative heat capacities, C α, as is shown in the particular case of the 2D seven-state Potts model where the exponent α = 0.14–0.18
The Current Canon in British Romantics Studies.
Linkin, Harriet Kramer
1991-01-01
Describes and reports on a survey of 164 U.S. universities to ascertain what is taught as the current canon of British Romantic literature. Asserts that the canon may now include Mary Shelley with the former standard six major male Romantic poets, indicating a significant emergence of a feminist perspective on British Romanticism in the classroom.…
Energy Technology Data Exchange (ETDEWEB)
Parvan, A.S. [Joint Institute for Nuclear Research, Bogoliubov Laboratory of Theoretical Physics, Dubna (Russian Federation); Horia Hulubei National Institute of Physics and Nuclear Engineering, Department of Theoretical Physics, Bucharest (Romania); Moldova Academy of Sciences, Institute of Applied Physics, Chisinau (Moldova, Republic of)
2015-09-15
In the present paper, the Tsallis statistics in the grand canonical ensemble was reconsidered in a general form. The thermodynamic properties of the nonrelativistic ideal gas of hadrons in the grand canonical ensemble was studied numerically and analytically in a finite volume and the thermodynamic limit. It was proved that the Tsallis statistics in the grand canonical ensemble satisfies the requirements of the equilibrium thermodynamics in the thermodynamic limit if the thermodynamic potential is a homogeneous function of the first order with respect to the extensive variables of state of the system and the entropic variable z = 1/(q - 1) is an extensive variable of state. The equivalence of canonical, microcanonical and grand canonical ensembles for the nonrelativistic ideal gas of hadrons was demonstrated. (orig.)
Singh, Parampreet
2015-01-01
The problem of obtaining canonical Hamiltonian structures from the equations of motion is studied in the context of the spatially flat Friedmann-Robertson-Walker models. Modifications to Raychaudhuri equation are implemented independently as quadratic and cubic terms of energy density without introducing additional degrees of freedom. Depending on its sign, modifications make gravity repulsive above a curvature scale for matter satisfying strong energy condition, or more attractive than in the classical theory. Canonical structure of the modified theories is determined demanding that the total Hamiltonian be a linear combination of gravity and matter Hamiltonians. Both of the repulsive modifications are found to yield singularity avoidance. In the quadratic repulsive case, the modified canonical phase space of gravity is a polymerized phase space with canonical momentum as inverse trigonometric function of Hubble rate; the canonical Hamiltonian can be identified with the effective Hamiltonian in loop quantum ...
Pitman, Jim
2002-01-01
This paper presents some general formulas for random partitions of a finite set derived by Kingman's model of random sampling from an interval partition generated by subintervals whose lengths are the points of a Poisson point process. These lengths can be also interpreted as the jumps of a subordinator, that is an increasing process with stationary independent increments. Examples include the two-parameter family of Poisson-Dirichlet models derived from the Poisson process of jumps of a stab...
Plasmid and chromosome partitioning: surprises from phylogeny
DEFF Research Database (Denmark)
Gerdes, Kenn; Møller-Jensen, Jakob; Bugge Jensen, Rasmus
2000-01-01
Plasmids encode partitioning genes (par) that are required for faithful plasmid segregation at cell division. Initially, par loci were identified on plasmids, but more recently they were also found on bacterial chromosomes. We present here a phylogenetic analysis of par loci from plasmids...... and chromosomes from prokaryotic organisms. All known plasmid-encoded par loci specify three components: a cis-acting centromere-like site and two trans-acting proteins that form a nucleoprotein complex at the centromere (i.e. the partition complex). The proteins are encoded by two genes in an operon...... that is autoregulated by the par-encoded proteins. In all cases, the upstream gene encodes an ATPase that is essential for partitioning. Recent cytological analyses indicate that the ATPases function as adaptors between a host-encoded component and the partition complex and thereby tether plasmids and chromosomal...
Singh, Parampreet; Soni, S. K.
2016-06-01
The problem of obtaining canonical Hamiltonian structures from the equations of motion, without any knowledge of the action, is studied in the context of the spatially flat Friedmann, ‘Robertson’, and Walker models. Modifications to the Raychaudhuri equation are implemented independently as quadratic and cubic terms of energy density without introducing additional degrees of freedom. Depending on their sign, modifications make gravity repulsive above a curvature scale for matter satisfying strong energy conditions, or more attractive than in the classical theory. The canonical structure of the modified theories is determined by demanding that the total Hamiltonian be a linear combination of gravity and matter Hamiltonians. In the quadratic repulsive case, the modified canonical phase space of gravity is a polymerized phase space with canonical momentum as inverse a trigonometric function of the Hubble rate; the canonical Hamiltonian can be identified with the effective Hamiltonian in loop quantum cosmology. The repulsive cubic modification results in a ‘generalized polymerized’ canonical phase space. Both the repulsive modifications are found to yield singularity avoidance. In contrast, the quadratic and cubic attractive modifications result in a canonical phase space in which canonical momentum is nontrigonometric and singularities persist. Our results hint at connections between the repulsive/attractive nature of modifications to gravity arising from the gravitational sector and polymerized/non polymerized gravitational phase space.
Extending canonical Monte Carlo methods
Velazquez, L.; Curilef, S.
2010-02-01
In this paper, we discuss the implications of a recently obtained equilibrium fluctuation-dissipation relation for the extension of the available Monte Carlo methods on the basis of the consideration of the Gibbs canonical ensemble to account for the existence of an anomalous regime with negative heat capacities C < 0. The resulting framework appears to be a suitable generalization of the methodology associated with the so-called dynamical ensemble, which is applied to the extension of two well-known Monte Carlo methods: the Metropolis importance sampling and the Swendsen-Wang cluster algorithm. These Monte Carlo algorithms are employed to study the anomalous thermodynamic behavior of the Potts models with many spin states q defined on a d-dimensional hypercubic lattice with periodic boundary conditions, which successfully reduce the exponential divergence of the decorrelation time τ with increase of the system size N to a weak power-law divergence \\tau \\propto N^{\\alpha } with α≈0.2 for the particular case of the 2D ten-state Potts model.
A Family of Trigonometrically-fitted Partitioned Runge-Kutta Symplectic Methods
International Nuclear Information System (INIS)
We are presenting a family of trigonometrically fitted partitioned Runge-Kutta symplectic methods of fourth order with six stages. The solution of the one dimensional time independent Schroedinger equation is considered by trigonometrically fitted symplectic integrators. The Schroedinger equation is first transformed into a Hamiltonian canonical equation. Numerical results are obtained for the one-dimensional harmonic oscillator and the exponential potential
Quantum canonical transformations in star-product formalism
International Nuclear Information System (INIS)
We study construction of the star-product version of three basic quantum canonical transformations which are known as the generators of the full canonical algebra. By considering the fact that star-product of c-number phase-space functions is in complete isomorphism to Hilbert-space operator algebra, it is shown that while the constructions of gauge and point transformations are immediate, generator of the interchanging transformation deforms this isomorphism. As an alternative approach, we study all of them within the deformed form. How to transform any c-number function under linear-nonlinear transformations and the intertwining method are shown within this argument as the complementary subjects of the text
Management of pediatric radiation dose using Canon digital radiography
International Nuclear Information System (INIS)
A Canon CXDI-11 digital radiography (DR) system has been in use at Shands Hospital at the University of Florida for the past 2 1/2 years. A first clinical implementation phase was utilized to develop imaging protocols for adult patients, with a second phase incorporating pediatric chest and abdominal studies a few months later. This paper describes some of the steps taken during the modality implementation stages, as well as the methodologies and procedures utilized to monitor compliance by the technologists. The Canon DR system provides the technologist with an indication of the radiation exposure received by the detector (and thus of the patient dose) by means of an indirect exposure level number called the reached exposure (REX) value. The REX value is calculated by the system based on the default grayscale curve preselected for a given anatomical view and used by the system to optimize the appearance of the image. The brightness and contrast of the image can be modified by the user at the QC/control screen for the purpose of improving the appearance of the image. Such changes modify the actual grayscale curve (position and slope, respectively) and thus the calculated REX value. Thus, undisciplined use of the brightness and contrast functions by the technologist can render the REX value meaningless as an exposure indicator. The paper also shows how it is possible to calibrate AEC (phototimer) systems for use with the Canon DR system, and utilize the REX value as a valuable dose indicator through proper training of technologists and strict, disciplined QC of studies. A team consisting of the site's medical physicist, radiologists, and technologists, as well as Canon engineers, can work together in properly calibrating and setting up the system for the purposes of monitoring patient doses (especially pediatric) in DR studies performed in a Canon DR system. (orig.)
Canonical pseudotensors, Sparling's form and Noether currents
International Nuclear Information System (INIS)
The canonical energy - momentum and spin pseudotensors of the Einstein theory are studied in two ways. First they are studied in the framework of Lagrangian formalism. It is shown, that for first order Lagrangian and rigid basis description the canonical energy - momentum, the canonical spin, and the Noether current are tensorial quantities, and the canonial energy - momentum and spin tensors satisfy the tensorial Belinfante-Rosenfeld equations. Then the differential geometric unification and reformulation of the previous different pseudotensorial approaches is given. Finally, for any vector field on the spacetime an (m-1) form, called the Noether form is defined. (K.A.) 34 refs
Partitioning Breaks Communities
Reid, Fergal; McDaid, Aaron; Hurley, Neil
Considering a clique as a conservative definition of community structure, we examine how graph partitioning algorithms interact with cliques. Many popular community-finding algorithms partition the entire graph into non-overlapping communities. We show that on a wide range of empirical networks, from different domains, significant numbers of cliques are split across the separate partitions produced by these algorithms. We then examine the largest connected component of the subgraph formed by retaining only edges in cliques, and apply partitioning strategies that explicitly minimise the number of cliques split. We further examine several modern overlapping community finding algorithms, in terms of the interaction between cliques and the communities they find, and in terms of the global overlap of the sets of communities they find. We conclude that, due to the connectedness of many networks, any community finding algorithm that produces partitions must fail to find at least some significant structures. Moreover, contrary to traditional intuition, in some empirical networks, strong ties and cliques frequently do cross community boundaries; much community structure is fundamentally overlapping and unpartitionable in nature.
Differential Forms on Log Canonical Spaces
Greb, Daniel; Kovacs, Sandor J; Peternell, Thomas
2010-01-01
The present paper is concerned with differential forms on log canonical varieties. It is shown that any p-form defined on the smooth locus of a variety with canonical or klt singularities extends regularly to any resolution of singularities. In fact, a much more general theorem for log canonical pairs is established. The proof relies on vanishing theorems for log canonical varieties and on methods of the minimal model program. In addition, a theory of differential forms on dlt pairs is developed. It is shown that many of the fundamental theorems and techniques known for sheaves of logarithmic differentials on smooth varieties also hold in the dlt setting. Immediate applications include the existence of a pull-back map for reflexive differentials, generalisations of Bogomolov-Sommese type vanishing results, and a positive answer to the Lipman-Zariski conjecture for klt spaces.
Regularized canonical correlation analysis with unlabeled data
Institute of Scientific and Technical Information of China (English)
Xi-chuan ZHOU; Hai-bin SHEN
2009-01-01
In standard canonical correlation analysis (CCA), the data from definite datasets are used to estimate their canonical correlation. In real applications, for example in bilingual text retrieval, it may have a great portion of data that we do not know which set it belongs to. This part of data is called unlabeled data, while the rest from definite datasets is called labeled data. We propose a novel method called regularized canonical correlation analysis (RCCA), which makes use of both labeled and unlabeled samples. Specifically, we learn to approximate canonical correlation as if all data were labeled. Then. we describe a generalization of RCCA for the multi-set situation. Experiments on four real world datasets, Yeast, Cloud, Iris, and Haberman, demonstrate that,by incorporating the unlabeled data points, the accuracy of correlation coefficients can be improved by over 30%.
Canonical equations of Hamilton with beautiful symmetry
Liang, Guo; Guo, Qi
2012-01-01
The Hamiltonian formulation plays the essential role in constructing the framework of modern physics. In this paper, a new form of canonical equations of Hamilton with the complete symmetry is obtained, which are valid not only for the first-order differential system, but also for the second-order differential system. The conventional form of the canonical equations without the symmetry [Goldstein et al., Classical Mechanics, 3rd ed, Addison-Wesley, 2001] are only for the second-order differe...
Heisenberg Uncertainty Relation for Three Canonical Observables
Kechrimparis, Spiros; Weigert, Stefan
2014-01-01
Uncertainty relations provide fundamental limits on what can be said about the properties of quantum systems. For a quantum particle, the commutation relation of position and momentum observables entails Heisenberg's uncertainty relation. A third observable is presented which satisfies canonical commutation relations with both position and momentum. The resulting triple of pairwise canonical observables gives rise to a Heisenberg-type uncertainty relation for the product of three standard dev...
Directory of Open Access Journals (Sweden)
Alexander M Many
Full Text Available The characterization of mammary stem cells, and signals that regulate their behavior, is of central importance in understanding developmental changes in the mammary gland and possibly for targeting stem-like cells in breast cancer. The canonical Wnt/β-catenin pathway is a signaling mechanism associated with maintenance of self-renewing stem cells in many tissues, including mammary epithelium, and can be oncogenic when deregulated. Wnt1 and Wnt3a are examples of ligands that activate the canonical pathway. Other Wnt ligands, such as Wnt5a, typically signal via non-canonical, β-catenin-independent, pathways that in some cases can antagonize canonical signaling. Since the role of non-canonical Wnt signaling in stem cell regulation is not well characterized, we set out to investigate this using mammosphere formation assays that reflect and quantify stem cell properties. Ex vivo mammosphere cultures were established from both wild-type and Wnt1 transgenic mice and were analyzed in response to manipulation of both canonical and non-canonical Wnt signaling. An increased level of mammosphere formation was observed in cultures derived from MMTV-Wnt1 versus wild-type animals, and this was blocked by treatment with Dkk1, a selective inhibitor of canonical Wnt signaling. Consistent with this, we found that a single dose of recombinant Wnt3a was sufficient to increase mammosphere formation in wild-type cultures. Surprisingly, we found that Wnt5a also increased mammosphere formation in these assays. We confirmed that this was not caused by an increase in canonical Wnt/β-catenin signaling but was instead mediated by non-canonical Wnt signals requiring the receptor tyrosine kinase Ror2 and activity of the Jun N-terminal kinase, JNK. We conclude that both canonical and non-canonical Wnt signals have positive effects promoting stem cell activity in mammosphere assays and that they do so via independent signaling mechanisms.
Refining inflation using non-canonical scalars
Energy Technology Data Exchange (ETDEWEB)
Unnikrishnan, Sanil; Sahni, Varun [Inter-University Centre for Astronomy and Astrophysics, Post Bag 4, Ganeshkhind, Pune 411 007 (India); Toporensky, Aleksey, E-mail: sanil@iucaa.ernet.in, E-mail: varun@iucaa.ernet.in, E-mail: atopor@rambler.ru [Sternberg Astronomical Institute, Moscow State University, Universitetsky Prospekt, 13, Moscow 119992 (Russian Federation)
2012-08-01
This paper revisits the Inflationary scenario within the framework of scalar field models possessing a non-canonical kinetic term. We obtain closed form solutions for all essential quantities associated with chaotic inflation including slow roll parameters, scalar and tensor power spectra, spectral indices, the tensor-to-scalar ratio, etc. We also examine the Hamilton-Jacobi equation and demonstrate the existence of an inflationary attractor. Our results highlight the fact that non-canonical scalars can significantly improve the viability of inflationary models. They accomplish this by decreasing the tensor-to-scalar ratio while simultaneously increasing the value of the scalar spectral index, thereby redeeming models which are incompatible with the cosmic microwave background (CMB) in their canonical version. For instance, the non-canonical version of the chaotic inflationary potential, V(φ) ∼ λφ{sup 4}, is found to agree with observations for values of λ as large as unity! The exponential potential can also provide a reasonable fit to CMB observations. A central result of this paper is that steep potentials (such as V∝φ{sup −n}) usually associated with dark energy, can drive inflation in the non-canonical setting. Interestingly, non-canonical scalars violate the consistency relation r = −8n{sub T}, which emerges as a smoking gun test for this class of models.
Canonical quantization of gravity without 'frozen formalism'
International Nuclear Information System (INIS)
We write down a quantum gravity equation which generalizes the Wheeler-DeWitt one in view of including a time dependence in the wave functional. The obtained equation provides a consistent canonical quantization of the 3-geometries resulting from a 'gauge-fixing' (3+1)-slicing of the space-time. Our leading idea relies on a criticism to the possibility that, in a quantum space-time, the notion of a (3+1)-slicing formalism (underlying the Wheeler-DeWitt approach) has yet a precise physical meaning. As solution to this problem we propose of adding to the gravity-matter action the so-called kinematical action (indeed in its reduced form, as implemented in the quantum regime), and then we impose the new quantum constraints. As consequence of this revised approach, the quantization procedure of the 3-geometries takes place in a fixed reference frame and the wave functional acquires a time evolution along a one-parameter family of spatial hypersurfaces filling the space-time. We show how the states of the new quantum dynamics can be arranged into an Hilbert space, whose associated inner product induces a conserved probability notion for the 3-geometries. Finally, since the constraints we quantize violate the classical symmetries (i.e., the vanishing nature of the super-Hamiltonian), then a key result is to find a (non-physical) restriction on the initial wave functional phase, ensuring that general relativity outcomes when taking the appropriate classical limit. However, we propose a physical interpretation of the kinematical variables which, based on the analogy with the so-called Gaussian reference fluid, makes allowance even for such classical symmetry violation
Canonical form of Euler-Lagrange equations and gauge symmetries
International Nuclear Information System (INIS)
The structure of the Euler-Lagrange equations for a general Lagrangian theory (e.g. singular, with higher derivatives) is studied. For these equations we present a reduction procedure to the so-called canonical form. In the canonical form the equations are solved with respect to highest-order derivatives of nongauge coordinates, whereas gauge coordinates and their derivatives enter the right-hand sides of the equations as arbitrary functions of time. The reduction procedure reveals constraints in the Lagrangian formulation of singular systems and, in that respect, is similar to the Dirac procedure in the Hamiltonian formulation. Moreover, the reduction procedure allows one to reveal the gauge identities between the Euler-Lagrange equations. Thus, a constructive way of finding all the gauge generators within the Lagrangian formulation is presented. At the same time, it is proved that for local theories all the gauge generators are local in time operators
A new method for counting trees with vertex partition
Institute of Scientific and Technical Information of China (English)
2008-01-01
A direct and elementary method is provided in this paper for counting trees with vertex partition instead of recursion, generating function, functional equation, Lagrange inversion, and matrix methods used before.
Generating Primes Using Partitions
Pittu, Ganesh Reddy
2015-01-01
This paper presents a new technique of generating large prime numbers using a smaller one by employing Goldbach partitions. Experiments are presented showing how this method produces candidate prime numbers that are subsequently tested using either Miller Rabin or AKS primality tests.
Methods of weyl representation of the phase space and canonical transformations
International Nuclear Information System (INIS)
The author finds the structure of the kernel of a canonical transformation and a differential equation for the symbol of the intertwining operator. The symbol of a general linear canonical transformation is constructed in terms of a Cayley transformation of the symplectic transformation of the phase space. Its singularities and applications to group theory are studied. The Green's functions and spectral projectors of arbitrary quadratic systems are constructed using the classification methods of classical mechanics
Generalization of a few results in Integer Partitions
Dastidar, Manosij Ghosh
2011-01-01
In this paper, we generalize a few important results in Integer Partitions; namely the results known as Stanley's theorem and Elder's theorem, and the congruence results proposed by Ramanujan for the partition function. We generalize the results of Stanley and Elder from a fixed integer to an array of subsequent integers, and propose an analogue of Ramanujan's congruence relations for the `number of parts' function instead of the partition function. We also deduce the generating function for the `number of parts', and relate the technical results with their graphical interpretations through a novel use of the Ferrer's diagrams.
A canonical theory of dynamic decision-making
Directory of Open Access Journals (Sweden)
John eFox
2013-04-01
Full Text Available Decision-making behaviour is studied in many very different fields, from medicine and economics to psychology and neuroscience, with major contributions from mathematics and statistics, computer science, AI and other technical disciplines. However the conceptualisation of what decision-making is and methods for studying it vary greatly and this has resulted in fragmentation of the field. A theory that can accommodate various perspectives may facilitate interdisciplinary working. We present such a theory in which decision-making is articulated as a set of canonical functions that are sufficiently general to accommodate diverse viewpoints, yet sufficiently precise that they can be instantiated in different ways for specific theoretical or practical purposes. The canons cover the whole decision cycle, from the framing of a decision based on the goals, beliefs, and background knowledge of the decision maker to the formulation of decision options, establishing preferences over them, and making commitments. Commitments can lead to the initiation of new decisions and any step in the cycle can incorporate reasoning about previous decisions and the rationales for them, and lead to revising or abandoning existing commitments. The theory situates decision making with respect to other high-level cognitive capabilities like problem-solving, planning and collaborative decision-making. The canonical approach is assessed in three domains: cognitive and neuro-psychology, artificial intelligence, and decision engineering.
DNA Partitioning in Confining Nanofluidic Slits
Greenier, Madeline; Levy, Stephen
We measure the partitioning of double stranded DNA molecules in moderately and strongly confining nanofluidic slit-like structures. Using fluorescent microscopy, the free energy penalty of confinement is inferred by comparing the concentration of DNA molecules in adjoining slits of different depths. These depths range in size from several persistence lengths to the DNA molecule's radius of gyration. The partition coefficient is determined as a function of the slit depth, DNA contour length, and DNA topology. We compare our results to theory and Monte Carlo simulations that predict the loss of free energy for ideal and semiflexible excluded volume polymers confined between parallel plates.
Universal canonical entropy for gravitating systems
Indian Academy of Sciences (India)
Ashok Chatterjee; Parthasarathi Majumdar
2004-10-01
The thermodynamics of general relativistic systems with boundary, obeying a Hamiltonian constraint in the bulk, is determined solely by the boundary quantum dynamics, and hence by the area spectrum. Assuming, for large area of the boundary, (a) an area spectrum as determined by non-perturbative canonical quantum general relativity (NCQGR), (b) an energy spectrum that bears a power law relation to the area spectrum, (c) an area law for the leading order microcanonical entropy, leading thermal fluctuation corrections to the canonical entropy are shown to be logarithmic in area with a universal coefficient. Since the microcanonical entropy also has universal logarithmic corrections to the area law (from quantum space-time fluctuations, as found earlier) the canonical entropy then has a universal form including logarithmic corrections to the area law. This form is shown to be independent of the index appearing in assumption (b). The index, however, is crucial in ascertaining the domain of validity of our approach based on thermal equilibrium.
Covariant Gauge Fixing and Canonical Quantization
McKeon, D G C
2011-01-01
Theories that contain first class constraints possess gauge invariance which results in the necessity of altering the measure in the associated quantum mechanical path integral. If the path integral is derived from the canonical structure of the theory, then the choice of gauge conditions used in constructing Faddeev's measure cannot be covariant. This shortcoming is normally overcome either by using the "Faddeev-Popov" quantization procedure, or by the approach of Batalin-Fradkin-Fradkina-Vilkovisky, and then demonstrating that these approaches are equivalent to the path integral constructed from the canonical approach with Faddeev's measure. We propose in this paper an alternate way of defining the measure for the path integral when it is constructed using the canonical procedure for theories containing first class constraints and that this new approach can be used in conjunction with covariant gauges. This procedure follows the Faddeev-Popov approach, but rather than working with the form of the gauge tran...
The random-variable canonical distribution
International Nuclear Information System (INIS)
An alternative interpretation to Gibbs' concept of the canonical distribution for an ensemble of systems in statistical equilibrium is proposed. Whereas Gibbs' theory is based upon a consideration of systems subject to dynamical law, the present analysis relies neither on the classical equations of motion nor makes use of any a priori probability of a complexion; rather, it makes avail of the basic algebra of random variables and, specifically, invokes the law of large numbers. Thereby, a canonical distribution is derived which describes a macrosystem in probabilistic, rather than deterministic, terms, and facilitates the understanding of energy fluctuations which occur in macrosystems at an overall constant ensemble temperature. A discussion is given of a modified form of the Gibbs canonical distribution which takes full account of the effects of random energy fluctuations. It is demonstrated that the results from this modified analysis are entirely consonant with those derived from the random-variable approach. (author)
A Canonical Analysis of the Massless Superparticle
McKeon, D G C
2012-01-01
The canonical structure of the action for a massless superparticle is considered in d = 2 + 1 and d = 3 + 1 dimensions. This is done by examining the contribution to the action of each of the components of the spinor {\\theta} present; no attempt is made to maintain manifest covariance. Upon using the Dirac Bracket to eliminate the second class constraints arising from the canonical momenta associated with half of these components, we find that the remaining components have canonical momenta that are all first class constraints. From these first class constraints, it is possible to derive the generator of half of the local Fermionic {\\kappa}-symmetry of Siegel; which half is contingent upon the choice of which half of the momenta associated with the components of {\\theta} are taken to be second class constraints. The algebra of the generator of this Fermionic symmetry transformation is examined.
The use and origin of the (Old and New Testament as Christianity’s canon
Directory of Open Access Journals (Sweden)
Andries G. van Aarde
2012-01-01
Full Text Available This article explained the valuation of Christian believers with regard to the Christian Bible a ‘Holy Scripture’. In the article the notion ‘Scriptural authority’ was connected with an understanding of both the origin and use of the Christian canon. The article described the origin of the Bible in light of the supposition that the Bible functions as (1 book of theology, as well as (2 book of believers and as (3 book of the church. The article consisted of references to the role of the Old Testament and the New Testament canonical collections and the role of ecclesial synodal decisions. It also obtained a graphical overview of the history and dates of the New Testament writings as a canonical list. The article concluded with a reflection on the relevance for the use and authority of the Bible, seen from the perspective of the use and origin of the Bible as Christianity’s canon.
A field theory approach to the evolution of canonical helicity and energy
You, Setthivoine
2016-01-01
A redefinition of the Lagrangian of a multi-particle system in fields reformulates the single-particle, kinetic, and fluid equations governing fluid and plasma dynamics as a single set of generalized Maxwell's equations and Ohm's law for canonical force-fields. The Lagrangian includes new terms representing the coupling between the motion of particle distributions, between distributions and electromagnetic fields, with relativistic contributions. The formulation shows that the concepts of self-organization and canonical helicity transport are applicable across single-particle, kinetic, and fluid regimes, at classical and relativistic scales. The theory gives the basis for comparing canonical helicity change to energy change in general systems. For example, in a fixed, isolated system subject to non-conservative forces, a species' canonical helicity changes less than total energy only if gradients in density or distribution function are shallow.
A field theory approach to the evolution of canonical helicity and energy
You, S.
2016-07-01
A redefinition of the Lagrangian of a multi-particle system in fields reformulates the single-particle, kinetic, and fluid equations governing fluid and plasma dynamics as a single set of generalized Maxwell's equations and Ohm's law for canonical force-fields. The Lagrangian includes new terms representing the coupling between the motion of particle distributions, between distributions and electromagnetic fields, with relativistic contributions. The formulation shows that the concepts of self-organization and canonical helicity transport are applicable across single-particle, kinetic, and fluid regimes, at classical and relativistic scales. The theory gives the basis for comparing canonical helicity change to energy change in general systems. For example, in a fixed, isolated system subject to non-conservative forces, a species' canonical helicity changes less than total energy only if gradients in density or distribution function are shallow.
Partitional clustering algorithms
2015-01-01
This book summarizes the state-of-the-art in partitional clustering. Clustering, the unsupervised classification of patterns into groups, is one of the most important tasks in exploratory data analysis. Primary goals of clustering include gaining insight into, classifying, and compressing data. Clustering has a long and rich history that spans a variety of scientific disciplines including anthropology, biology, medicine, psychology, statistics, mathematics, engineering, and computer science. As a result, numerous clustering algorithms have been proposed since the early 1950s. Among these algorithms, partitional (nonhierarchical) ones have found many applications, especially in engineering and computer science. This book provides coverage of consensus clustering, constrained clustering, large scale and/or high dimensional clustering, cluster validity, cluster visualization, and applications of clustering. Examines clustering as it applies to large and/or high-dimensional data sets commonly encountered in reali...
Partitioned Triangular Tridiagonalization
Czech Academy of Sciences Publication Activity Database
Rozložník, Miroslav; Shklarski, G.; Toledo, S.
2011-01-01
Roč. 37, č. 4 (2011), 38:1-38:16. ISSN 0098-3500 R&D Projects: GA AV ČR IAA100300802 Institutional research plan: CEZ:AV0Z10300504 Keywords : algorithms * performance * symmetric indefinite matrices * tridiagonalization * Aasen's tridiagonalization * Parlett-Reid tridiagonalization * partitioned factorizations * recursive factorizations Subject RIV: BA - General Mathematics Impact factor: 1.922, year: 2011
Canonical quantization of generally covariant systems
International Nuclear Information System (INIS)
Kretschmann (1917) argued that general relativity does not satisfy any relativity principle and that it is actually a theory of absolute space-time. The issues raised by Kretschmann, that of Hamiltonian dynamics and of canonical quantization of generally covariant systems, are discussed. The questions raised are: what is the role of space-time diffeomorphisms in Hamiltonian dynamics of generally covariant systems, what is the role of isometries in Hamiltonian dynamics of such systems and what happens to both problems in canonical quantization. (author)
Periodic Schur process, cylindric partitions and N=2* theory
International Nuclear Information System (INIS)
Type IIA string theory compactified on an elliptic CY3-fold gives rise to N=2U(1) gauge theory with an adjoint hypermultiplet. We study the refined open and closed topological string partition functions of this geometry using the refined topological vertex. We show that these partition functions, open and closed, are examples of periodic Schur process and are related to the generating function of the cylindric partitions if the Kaehler parameters are quantized in units of string coupling. The level-rank duality appears as the exchange symmetry of the two Kaehler parameters of the elliptic CY3-fold.
Development of partitioning method
International Nuclear Information System (INIS)
A partitioning method has been developed under the concepts of separation of nuclides in high level nuclear fuel reprocessing liquid waste according to their half lives and radioactive toxicity and of disposal of them by suitable methods. In the partitioning process, which has been developed in JAERI, adoption of solvent extraction process with DIDPA (di-isodecyl phosphoric acid) has been studied for actinides separation. The present paper mainly describes studies on back extraction behavior of Np(IV), Pu(IV) and U(VI) in DIDPA. Most experiments were carried out according to following procedure. These actinides were extracted from 0.5 M nitric acid with DIDPA, where nitric acid concentration in HLW is expected to be adjusted to this value prior to actinides extraction in the partitioning process, and back-extracted with various reagents such as oxalic acid. The experimental results show that distribution ratios of Np(IV) and Pu(IV) can be reduced to less than unity with 1 M oxalic acid and those of U(VI) and Np(IV) with 5 M phosphoric acid. From results of these studies and previous research on Am and Cm, following possibilities were confirmed ; U, Pu, Np, Am and Cm, which are major actinides in HLW, can be extracted simultaneously with DIDPA, and they can be removed from DIDPA with various reagents. (nitric acid for Am and Cm, oxalic acid for Np and Pu, and phosphoric acid for U respectively). (author)
Canonical vs. micro-canonical sampling methods in a 2D Ising model
International Nuclear Information System (INIS)
Canonical and micro-canonical Monte Carlo algorithms were implemented on a 2D Ising model. Expressions for the internal energy, U, inverse temperature, Z, and specific heat, C, are given. These quantities were calculated over a range of temperature, lattice sizes, and time steps. Both algorithms accurately simulate the Ising model. To obtain greater than three decimal accuracy from the micro-canonical method requires that the more complicated expression for Z be used. The overall difference between the algorithms is small. The physics of the problem under study should be the deciding factor in determining which algorithm to use. 13 refs., 6 figs., 2 tabs
Kuidas Canon suureks kasvas / Andres Eilart
Eilart, Andres
2004-01-01
Jaapani kaamerate ja büroomasinate tootja Canon Groupi arengust, tegevusest kolmes regioonis - USA-s, Euroopas ja Aasias ning ettevõtte pikaajalise edu põhjustest - ärifilosoofiast ning ajastatud tootearendusest. Vt. samas: Firma esialgne nimi oli Kwanon; Konkurendid koonduvad
On the canonical treatment of Lagrangian constraints
International Nuclear Information System (INIS)
The canonical treatment of dynamic systems with manifest Lagrangian constraints proposed by Berezin is applied to concrete examples: a special Lagrangian linear in velocities, relativistic particles in proper time gauge, a relativistic string in orthonormal gauge, and the Maxwell field in the Lorentz gauge
On the generalized Lorenz canonical form
Czech Academy of Sciences Publication Activity Database
Čelikovský, Sergej; Guanrong, Ch.
2005-01-01
Roč. 26, č. 5 (2005), s. 1271-1276. ISSN 0960-0779 R&D Projects: GA ČR GA102/05/0011; GA MŠk 1P05LA262 Institutional research plan: CEZ:AV0Z10750506 Keywords : chaos * synchronization * canonical form Subject RIV: BC - Control Systems Theory Impact factor: 1.938, year: 2005
Infants' Recognition of Objects Using Canonical Color
Kimura, Atsushi; Wada, Yuji; Yang, Jiale; Otsuka, Yumiko; Dan, Ippeita; Masuda, Tomohiro; Kanazawa, So; Yamaguchi, Masami K.
2010-01-01
We explored infants' ability to recognize the canonical colors of daily objects, including two color-specific objects (human face and fruit) and a non-color-specific object (flower), by using a preferential looking technique. A total of 58 infants between 5 and 8 months of age were tested with a stimulus composed of two color pictures of an object…
Canonical duties, liabilities of trustees and administrators.
Morrisey, F G
1985-06-01
The new Code of Canon Law outlines a number of duties of those who have responsibility for administering the Church's temporal goods. Before assuming office, administrators must pledge to be efficient and faithful, and they must prepare an inventory of goods belonging to the juridic person they serve. Among their duties, administrators must: Ensure that adequate insurance is provided; Use civilly valid methods to protect canonical ownership of the goods; Observe civil and canon law prescriptions as well as donors' intentions; Collect and safeguard revenues, repay debts, and invest funds securely; Maintain accurate records, keep documents secure, and prepare an annual budget; Prepare an annual report and present it to the Ordinary where prescribed; Observe civil law concerning labor and social policy, and pay employees a just and decent wage. Administrators who carry out acts that are invalid canonically are liable for such acts. The juridic person is not liable, unless it derived benefit from the transaction. Liability is especially high when the sale of property is involved or when a contract is entered into without proper cannonical consent. Although Church law is relatively powerless to punish those who have been negligent, stewards, administrators, and trustees must do all they can to be truthful to the responsibility with which they have been entrusted. PMID:10271510
Conservation laws of semidiscrete canonical Hamiltonian equations
International Nuclear Information System (INIS)
There are many evolution partial differential equations which can be cast into Hamiltonian form. Conservation laws of these equations are related to one-parameter Hamiltonian symmetries admitted by the PDEs. The same result holds for semidiscrete Hamiltonian equations. In this paper we consider semidiscrete canonical Hamiltonian equations. Using symmetries, we find conservation laws for the semidiscretized nonlinear wave equation and Schroedinger equation. (author)
Kelvin's Canonical Circulation Theorem in Hall Magnetohydrodynamics
Shivamoggi, B K
2016-01-01
The purpose of this paper is to show that, thanks to the restoration of the legitimate connection between the current density and the plasma flow velocity in Hall magnetohydrodynamics (MHD), Kelvin's Circulation Theorem becomes valid in Hall MHD. The ion-flow velocity in the usual circulation integral is now replaced by the canonical ion-flow velocity.
Canonical transformation for trapped/passing guiding-center orbits in axisymmetric tokamak geometry
Energy Technology Data Exchange (ETDEWEB)
Brizard, Alain J. [Department of Physics, Saint Michael' s College, Colchester, Vermont 05439 (United States); Duthoit, François-Xavier [CEA, IRFM, F-13108 Saint-Paul-lez-Durance (France); SNU Division of Graduate Education for Sustainabilization of Foundation Energy, Seoul National University, Seoul 151-742 (Korea, Republic of)
2014-05-15
The generating function for the canonical transformation from the parallel canonical coordinates (s,p{sub ||}) to the action-angle coordinates (ζ, J) for trapped/passing guiding-center orbits in axisymmetric tokamak geometry is presented. Drawing on the analogy between the phase-space portraits of the librating/rotating pendulum and the trapped/passing guiding-center orbits, the generating function is expressed in terms of the Jacobi zeta function, which can then readily be used to obtain an explicit expression for the bounce-center transformation for trapped/passing-particle guiding-center orbits in axisymmetric tokamak geometry.
Ménager, Christine; Guemghar, Dihya; Cabuil, Valérie; Lesieur, Sylviane
2010-10-01
The present study deals with the morphological modifications of giant dioleoyl phosphatidylcholine vesicles (DOPC GUVs) induced by the nonionic surfactant n-octyl β,D-glucopyranoside at sublytic levels, i.e., in the first steps of the vesicle-to-micelle transition process, when surfactant inserts into the vesicle bilayer without disruption. Experimental conditions were perfected to exactly control the surfactant bilayer composition of the vesicles, in line with former work focused on the mechanical properties of the membrane of magnetic-fluid-loaded DOPC GUVs submitted to a magnetic field. The purpose here was to systematically examine, in the absence of any external mechanical constraint, the dynamics of giant vesicle shape and membrane deformations as a function of surfactant partitioning between the aqueous phase and the lipid membrane, beforehand established by turbidity measurements from small unilamellar vesicles. PMID:20825201
Canonical brackets of a toy model for the Hodge theory without its canonical conjugate momenta
Shukla, D; Malik, R P
2014-01-01
We consider the toy model of a rigid rotor as an example of the Hodge theory within the framework of the Becchi-Rouet-Stora-Tyutin (BRST) formalism and show that the internal symmetries of this theory lead to the derivation of canonical brackets amongst the creation and annihilation operators of the dynamical variables where the definition of the canonical conjugate momenta is not required. We invoke only the spin-statistics theorem, normal ordering and basic concepts of continuous symmetries (and their generators) to derive the canonical brackets for the model of a one (0 + 1)-dimensional (1D) rigid rotor without using the definition of the canonical conjugate momenta anywhere. Our present method of derivation of the basic brackets is conjectured to be true for a class of theories that provide a set of tractable physical examples for the Hodge theory.
Canonical brackets of a toy model for the Hodge theory without its canonical conjugate momenta
Shukla, D.; Bhanja, T.; Malik, R. P.
2015-07-01
We consider the toy model of a rigid rotor as an example of the Hodge theory within the framework of Becchi-Rouet-Stora-Tyutin (BRST) formalism and show that the internal symmetries of this theory lead to the derivation of canonical brackets amongst the creation and annihilation operators of the dynamical variables where the definition of the canonical conjugate momenta is not required. We invoke only the spin-statistics theorem, normal ordering and basic concepts of continuous symmetries (and their generators) to derive the canonical brackets for the model of a one (0 + 1)-dimensional (1D) rigid rotor without using the definition of the canonical conjugate momenta anywhere. Our present method of derivation of the basic brackets is conjectured to be true for a class of theories that provide a set of tractable physical examples for the Hodge theory.
Refined topological vertex, cylindric partitions and U(1) adjoint theory
International Nuclear Information System (INIS)
We study the partition function of the compactified 5D U(1) gauge theory (in the Ω-background) with a single adjoint hypermultiplet, calculated using the refined topological vertex. We show that this partition function is an example a periodic Schur process and is a refinement of the generating function of cylindric plane partitions. The size of the cylinder is given by the mass of adjoint hypermultiplet and the parameters of the Ω-background. We also show that this partition function can be written as a trace of operators which are generalizations of vertex operators studied by Carlsson and Okounkov. In the last part of the paper we describe a way to obtain (q,t) identities using the refined topological vertex.
Canonical brackets of a toy model for the Hodge theory without its canonical conjugate momenta
D Shukla; Bhanja, T.; Malik, R. P.
2014-01-01
We consider the toy model of a rigid rotor as an example of the Hodge theory within the framework of the Becchi-Rouet-Stora-Tyutin (BRST) formalism and show that the internal symmetries of this theory lead to the derivation of canonical brackets amongst the creation and annihilation operators of the dynamical variables where the definition of the canonical conjugate momenta is not required. We invoke only the spin-statistics theorem, normal ordering and basic concepts of continuous symmetries...
Crystal/liquid partitioning in augite - Effects of cooling rate
Gamble, R. P.; Taylor, L. A.
1980-01-01
The partitioning of major and minor elements between augite and melt was determined as a function of cooling rate for two high-titanium basalt compositions. The results of this study of lunar rock systems 10017 and 75055 were compared with the results of other kinetic studies of augite-liquid partitioning in other rock systems. It was found that the partitioning of major elements (i.e., Ca, Fe, Mg) is essentially rate independent and is insensitive to bulk rock composition and to the nature and order of appearance of coexisting phases for cooling rates of less than 100 C/hr. The partitioning behavior of minor elements (i.e., Al, Cr, Ti) for the same range of cooling rates is complex, being dependent on cooling rate and bulk rock composition. Consideration of these factors is important when augite chemistry and/or partitioning behavior are used in modeling certain magmatic processes or in estimating the thermal history of basaltic rocks.
Osipov, Vitaly; Sanders, Peter
2010-01-01
We present a multi-level graph partitioning algorithm based on the extreme idea to contract only a single edge on each level of the hierarchy. This obviates the need for a matching algorithm and promises very good partitioning quality since there are very few changes between two levels. Using an efficient data structure and new flexible ways to break local search improvements early, we obtain an algorithm that scales to large inputs and produces the best known partitioning results for many in...
Development of partitioning method
International Nuclear Information System (INIS)
A partitioning method has been developed under the concepts of separating radioactive nuclides from a high-level waste according to their half lives and radioactive toxicity, and of disposing the waste safely. The partitioning test using about 18 liters (--220Ci) of the fuel reprocessing waste prepared at PNC has been started in October of 1982. In this test the behavior of radioactive nuclides was made clear. The present paper describes chemical behavior of non-radioactive elements contained in the high-level liquid waste in the extraction with di-isodecyl phosphoric acid (DIDPA). Distribution ratios of most of metal ions for DIDPA were less than 0.05, except that those of Mo, Zr and Fe were higher than 7. Ferric ion could not be back-extracted with 4 M HNO3, but with 0.5 M (COOH)2. In the extractiion with DIDPA, the third phase, which causes closing the settling banks or the flow paths in a mixer settler, was formed when the ferric ion concentration was over 0.02 M. This unfavorable phenomenon, however, was found to be suppressed by diluting the ferric ion concentration to lower than 0.01 M or by reducing ferric ion to ferrous ion. (author)
Triality and the grand canonical ensemble in QCD
International Nuclear Information System (INIS)
QCD in the usual finite temperature formulation is using the grand canonical ensemble with chemical potential zero. We demonstrate that this description may give wrong predictions. QCD in the canonical formulation does not explicitly break Z(3) symmetry. It behaves in this sense like pure gluonic QCD. There are no metastable states in the canonical ensemble description as predicted in the grand canonical ensemble formalism. ((orig.))
An introduction to the theory of canonical matrices
Turnbull, H W
2004-01-01
Thorough and self-contained, this penetrating study of the theory of canonical matrices presents a detailed consideration of all the theory's principal features. Topics include elementary transformations and bilinear and quadratic forms; canonical reduction of equivalent matrices; subgroups of the group of equivalent transformations; and rational and classical canonical forms. The final chapters explore several methods of canonical reduction, including those of unitary and orthogonal transformations. 1952 edition. Index. Appendix. Historical notes. Bibliographies. 275 problems.
Canonical analysis based on mutual information
DEFF Research Database (Denmark)
Nielsen, Allan Aasbjerg; Vestergaard, Jacob Schack
2015-01-01
Canonical correlation analysis (CCA) is an established multi-variate statistical method for finding similarities between linear combinations of (normally two) sets of multivariate observations. In this contribution we replace (linear) correlation as the measure of association between the linear...... combinations with the information theoretical measure mutual information (MI). We term this type of analysis canonical information analysis (CIA). MI allows for the actual joint distribution of the variables involved and not just second order statistics. While CCA is ideal for Gaussian data, CIA facilitates...... analysis of variables with different genesis and therefore different statistical distributions and different modalities. As a proof of concept we give a toy example. We also give an example with one (weather radar based) variable in the one set and eight spectral bands of optical satellite data in the...
DNA pattern recognition using canonical correlation algorithm
Indian Academy of Sciences (India)
B K Sarkar; Chiranjib Chakraborty
2015-10-01
We performed canonical correlation analysis as an unsupervised statistical tool to describe related views of the same semantic object for identifying patterns. A pattern recognition technique based on canonical correlation analysis (CCA) was proposed for finding required genetic code in the DNA sequence. Two related but different objects were considered: one was a particular pattern, and other was test DNA sequence. CCA found correlations between two observations of the same semantic pattern and test sequence. It is concluded that the relationship possesses maximum value in the position where the pattern exists. As a case study, the potential of CCA was demonstrated on the sequence found from HIV-1 preferred integration sites. The subsequences on the left and right flanking from the integration site were considered as the two views, and statistically significant relationships were established between these two views to elucidate the viral preference as an important factor for the correlation.
2010-01-01
Le numéro sept de notre revue réunit les collaborations d’Isabelle López García (posthume), transition intéressante entre canon littéraire, canon social et figuration des corps rendus monstrueux par le fléau du sida ; de Richard Cleminson, spécialiste de l’histoire de la sexualité (en annexe), ainsi que celles de plusieurs chercheures et chercheurs présent.e.s aux journées d’étude entre Toulouse et Tours : Cecilia González analyse le dialogue entre les “anciens et les modernes” à trav...
Rewriting Canonical Love Stories from the Peripheries
Yang, Karen Ya-Chu
2013-01-01
In her article "Rewriting Canonical Love Stories from the Peripheries" Karen Ya-Chu Yang compares postcolonial and postmodern intertextuality in Taiwanese and the Caribbean texts. Hsien-Yung Pai's "Wandering in the Garden, Waking from a Dream" (1966) and Tien-Hsin Chu's "Breakfast at Tiffany's" (1997) are two short stories which depict identity crises of first generation and second generation 外省人 (waishen gren, mainland immigrants). In these two texts disillusionment towards the center's roma...
On Complex Supermanifolds with Trivial Canonical Bundle
Groeger, Josua
2016-01-01
We give an algebraic characterisation for the triviality of the canonical bundle of a complex supermanifold in terms of a certain Batalin-Vilkovisky superalgebra structure. As an application, we study the Calabi-Yau case, in which an explicit formula in terms of the Levi-Civita connection is achieved. Our methods include the use of complex integral forms and the recently developed theory of superholonomy.
Canonical quantization of substrate-less fields
Gründler, Gerold
2015-01-01
An improved law for the canonical quantization of fields is presented, which is based on the distinction between fields which have a material substrate, and substrate-less fields. It is shown that the improved quantization method solves the (old) cosmological constant problem for all fields of the standard model of elementary particles and for the metric field, but not for the hypothetical inflaton fields, without compromising any of the achievements of the established quantum field theories.
THEOLOGY OF CANONS IN CATHOLIC UNIVERSITIES?
IVÁN FEDERICO MEJÍA A
2010-01-01
Is it useful today, or necessary, an interpretation of the Code of Canon Law from Christology? The article examines some opposition which consider as inappropriate to search for foundations or links from "outside" the Code itself and the normal legislative living tradition of the Catholic Church. The Second Vatican Council and Pope John Paul II sponsored a theological interpretation of the Code, and this article summarizes some features of the validation, method, and the successful applicatio...
Canonical Energy is Quantum Fisher Information
Lashkari, Nima
2015-01-01
In quantum information theory, Fisher Information is a natural metric on the space of perturbations to a density matrix, defined by calculating the relative entropy with the unperturbed state at quadratic order in perturbations. In gravitational physics, Canonical Energy defines a natural metric on the space of perturbations to spacetimes with a Killing horizon. In this paper, we show that the Fisher information metric for perturbations to the vacuum density matrix of a ball-shaped region B in a holographic CFT is dual to the canonical energy metric for perturbations to a corresponding Rindler wedge R_B of Anti-de-Sitter space. Positivity of relative entropy at second order implies that the Fisher information metric is positive definite. Thus, for physical perturbations to anti-de-Sitter spacetime, the canonical energy associated to any Rindler wedge must be positive. This second-order constraint on the metric extends the first order result from relative entropy positivity that physical perturbations must sat...
Extending canonical Monte Carlo methods: II
Velazquez, L.; Curilef, S.
2010-04-01
We have previously presented a methodology for extending canonical Monte Carlo methods inspired by a suitable extension of the canonical fluctuation relation C = β2langδE2rang compatible with negative heat capacities, C < 0. Now, we improve this methodology by including the finite size effects that reduce the precision of a direct determination of the microcanonical caloric curve β(E) = ∂S(E)/∂E, as well as by carrying out a better implementation of the MC schemes. We show that, despite the modifications considered, the extended canonical MC methods lead to an impressive overcoming of the so-called supercritical slowing down observed close to the region of the temperature driven first-order phase transition. In this case, the size dependence of the decorrelation time τ is reduced from an exponential growth to a weak power-law behavior, \\tau (N)\\propto N^{\\alpha } , as is shown in the particular case of the 2D seven-state Potts model where the exponent α = 0.14-0.18.
Juridic status: canonical provisions, possible applications.
Morrisey, F G
1986-09-01
The 1983 Code of Canon Law presents the basic legislation regarding juridic persons, which are entities brought into existence to assist in carrying out the Church's mission. Juridic persons by nature are perpetual and are not directly identified with their members. The private juridic person, a concept introduced in the 1983 code, operates collegially on behalf of its members or noncollegially on behalf of the things that constitute it. A ministry that receives private juridic status does not share as integrally in the Church's name. The latter therefore has more duties to fulfill in regard to observance of Church law, particularly that concerning the administration of temporal goods. The goods of a private juridic person, in contrast, are not ecclesiastical and thus are not subject to canon law. Instead, the private juridic persons' statutes provide norms for their administration. Canon law in establishing juridic persons enables the ministries they represent to last beyond the lives of those who initiated the ministries. Juridic persons offer both security and possibilities for concerted apostolic activity in the Church. PMID:10277620
India and Pakistan: Partition Lessons
DEFF Research Database (Denmark)
Kaur, Ravinder
2007-01-01
The violent territorial rupture of 1947 and its legacy reveal partition to be conceptually flawed and historically ill-grounded as a solution to political antagonism, says Ravinder Kaur.......The violent territorial rupture of 1947 and its legacy reveal partition to be conceptually flawed and historically ill-grounded as a solution to political antagonism, says Ravinder Kaur....
Yuan, Xue; Cao, Jay; He, Xiaoning; Serra, Rosa; Qu, Jun; Cao, Xu; Yang, Shuying
2016-01-01
Intraflagellar transport proteins (IFT) are required for hedgehog (Hh) signalling transduction that is essential for bone development, however, how IFT proteins regulate Hh signalling in osteoblasts (OBs) remains unclear. Here we show that deletion of ciliary IFT80 in OB precursor cells (OPC) in mice results in growth retardation and markedly decreased bone mass with impaired OB differentiation. Loss of IFT80 blocks canonical Hh–Gli signalling via disrupting Smo ciliary localization, but elevates non-canonical Hh–Gαi–RhoA–stress fibre signalling by increasing Smo and Gαi binding. Inhibition of RhoA and ROCK activity partially restores osteogenic differentiation of IFT80-deficient OPCs by inhibiting non-canonical Hh–RhoA–Cofilin/MLC2 signalling. Cytochalasin D, an actin destabilizer, dramatically restores OB differentiation of IFT80-deficient OPCs by disrupting actin stress fibres and promoting cilia formation and Hh–Gli signalling. These findings reveal that IFT80 is required for OB differentiation by balancing between canonical Hh–Gli and non-canonical Hh–Gαi–RhoA pathways and highlight IFT80 as a therapeutic target for craniofacial and skeletal abnormalities. PMID:26996322
Canonical RNA Pseudoknot Structures with Arc Length $\\geq 4$
Reidys, Christian M; Zhao, Albus Y Y
2010-01-01
In this paper, we compute the generating function of the arguably most important target class of folding algorithms into RNA pseudoknot structures. This class consists of $k$-noncrossing, canonical RNA structures having minimum arc length four and generalizes directly the canonical secondary structures, studied by Schuster {\\it et al.} \\cite{Schuster:98}. The combinatorics of this class is important since, in analogy to the case of secondary structures, generic properties of genotype phenotype maps into RNA pseudoknot structures, like shape space covering \\cite{Schuster:94} and neutral networks \\cite{Reidys:97a} are a result of the combinatorics and not of the particulars of energy parameters. Let ${\\sf Q}_k(n)$ denote the number of these structures over $n$ vertices. We derive exact enumeration results as well as the asymptotic formula ${\\sf Q}_k(n)\\sim c_k n^{-(k-1)^2-\\frac{k-1}{2}}(\\gamma_{\\theta,k})^{-n}$ for $k=3, ..., 9$ and derive a new proof of Schuster's result, ${\\sf Q}_2(n)\\sim 1.4848\\, n^{-3/2}\\,1...
The gauge-invariant canonical energy-momentum tensor
Directory of Open Access Journals (Sweden)
Lorcé Cédric
2016-01-01
Full Text Available The canonical energy-momentum tensor is often considered as a purely academic object because of its gauge dependence. However, it has recently been realized that canonical quantities can in fact be defined in a gauge-invariant way provided that strict locality is abandoned, the non-local aspect being dictacted in high-energy physics by the factorization theorems. Using the general techniques for the parametrization of non-local parton correlators, we provide for the first time a complete parametrization of the energy-momentum tensor (generalizing the purely local parametrizations of Ji and Bakker-Leader-Trueman used for the kinetic energy-momentum tensor and identify explicitly the parts accessible from measurable two-parton distribution functions (TMDs and GPDs. As by-products, we confirm the absence of model-independent relations between TMDs and parton orbital angular momentum, recover in a much simpler way the Burkardt sum rule and derive three similar new sum rules expressing the conservation of transverse momentum.
The gauge-invariant canonical energy-momentum tensor
Lorcé, Cédric
2016-03-01
The canonical energy-momentum tensor is often considered as a purely academic object because of its gauge dependence. However, it has recently been realized that canonical quantities can in fact be defined in a gauge-invariant way provided that strict locality is abandoned, the non-local aspect being dictacted in high-energy physics by the factorization theorems. Using the general techniques for the parametrization of non-local parton correlators, we provide for the first time a complete parametrization of the energy-momentum tensor (generalizing the purely local parametrizations of Ji and Bakker-Leader-Trueman used for the kinetic energy-momentum tensor) and identify explicitly the parts accessible from measurable two-parton distribution functions (TMDs and GPDs). As by-products, we confirm the absence of model-independent relations between TMDs and parton orbital angular momentum, recover in a much simpler way the Burkardt sum rule and derive three similar new sum rules expressing the conservation of transverse momentum.
The gauge-invariant canonical energy-momentum tensor
Lorcé, Cédric
2016-01-01
The canonical energy-momentum tensor is often considered as a purely academic object because of its gauge dependence. However, it has recently been realized that canonical quantities can in fact be defined in a gauge-invariant way provided that strict locality is abandoned, the non-local aspect being dictacted in high-energy physics by the factorization theorems. Using the general techniques for the parametrization of non-local parton correlators, we provide for the first time a complete parametrization of the energy-momentum tensor (generalizing the purely local parametrizations of Ji and Bakker-Leader-Trueman used for the kinetic energy-momentum tensor) and identify explicitly the parts accessible from measurable two-parton distribution functions (TMDs and GPDs). As by-products, we confirm the absence of model-independent relations between TMDs and parton orbital angular momentum, recover in a much simpler way the Burkardt sum rule and derive three similar new sum rules expressing the conservation of transv...
Theory of extreme correlations using canonical Fermions and path integrals
International Nuclear Information System (INIS)
The t–J model is studied using a novel and rigorous mapping of the Gutzwiller projected electrons, in terms of canonical electrons. The mapping has considerable similarity to the Dyson–Maleev transformation relating spin operators to canonical Bosons. This representation gives rise to a non Hermitian quantum theory, characterized by minimal redundancies. A path integral representation of the canonical theory is given. Using it, the salient results of the extremely correlated Fermi liquid (ECFL) theory, including the previously found Schwinger equations of motion, are easily rederived. Further, a transparent physical interpretation of the previously introduced auxiliary Greens function and the ‘caparison factor’, is obtained. The low energy electron spectral function in this theory, with a strong intrinsic asymmetry, is summarized in terms of a few expansion coefficients. These include an important emergent energy scale Δ0 that shrinks to zero on approaching the insulating state, thereby making it difficult to access the underlying very low energy Fermi liquid behavior. The scaled low frequency ECFL spectral function, related simply to the Fano line shape, has a peculiar energy dependence unlike that of a Lorentzian. The resulting energy dispersion obtained by maximization is a hybrid of a massive and a massless Dirac spectrum EQ∗∼γQ−√(Γ02+Q2), where the vanishing of Q, a momentum type variable, locates the kink minimum. Therefore the quasiparticle velocity interpolates between (γ∓1) over a width Γ0 on the two sides of Q=0, implying a kink there that strongly resembles a prominent low energy feature seen in angle resolved photoemission spectra (ARPES) of cuprate materials. We also propose novel ways of analyzing the ARPES data to isolate the predicted asymmetry between particle and hole excitations. -- Highlights: •Spectral function of the Extremely Correlated Fermi Liquid theory at low energy. •Electronic origin of low energy kinks in
Avicenna's Canon of Medicine: a look at health, public health, and environmental sanitation.
Saffari, Mohsen; Pakpour, Amir H
2012-12-01
Avicenna, a renowned Persian Muslim scientist has written numerous scientific papers and valuable medical books that are respected worldwide. For centuries his masterpiece, the "Canon of Medicine", has been used as a major medical reference. The Canon, as a prime encyclopedia on medicine is comprised of five books. In the introduction to the Canon, Avicenna has described the purpose of medicine as the preservation of health if it is already attained and its restoration when it is lost. He defines health as a trait or state, which results in the normal functioning of the human body and presumes that health is a steady state, whilst disease is more of a variable concept. Thus whenever we depart from a healthy state, we approach disease. A comparison of current views regarding definitions of health, disease and their components as defined by Avicenna could open new horizons for ancient, traditional medicine. The Canon contains numerous implications concerning the infrastructures of public health-related issues. For example the specifications of healthy water and air are well described in the "Canon of Medicine". To enable a better understanding of Avicenna's viewpoints about public health, we have briefly reviewed his perspective on the topics of health, disease, and environmental sanitation concerning water and air. PMID:23199255
Repeatability Using Automatic Tracing with Canon OCT- HS100 and Zeiss Cirrus HD-OCT 5000
Brautaset, Rune; Birkeldh, Ulrika; Frehr Alstig, Petra; Wikén, Petra; Nilsson, Maria
2016-01-01
Background Optical coherence tomography (OCT), can be used in clinical practice to provide high resolution cross-sectional images of the retina, optic disc and macula structure. These measurements can be useful for early detection, diagnosis, monitoring and treatment guidance for retinal diseases. Therefore, repeatability of measurements in OCT is of great importance. Methods Macula and optic disc parameters from the right eye of 30 healthy subjects were obtained twice with the Canon OCT-HS100 and Zeiss Cirrus HD-OCT 5000. Repeatability was evaluated by use of the coefficient of repeatability (CR) and the coefficient of repeatability as a percentage of the mean (CR%), and the obtained measurements were compared between the instruments. Results CR% of optic disc parameters ranged between 0.90 and 22.22% and 0.00 and 16.00% with the Canon and Zeiss OCT respectively. For macular parameters CR% ranged between 0.62 and 2.81% and 0.99 and 1.81% with the Canon and Zeiss OCT respectively. No statistical difference could be found when comparing the CR of all macular and disc measurements between the instruments. Compared to our previously published data repeatability has significantly improved with the inclusion of automatic tracking systems with both the Canon and Zeiss OCT. Conclusion Automatic tracking function improves repeatability in both Canon OCT-HS100 and Zeiss Cirrus HD-OCT 5000. However, measurements generated by the two instruments are still not interchangeable. PMID:26867021
Canonical group quantization and boundary conditions
Energy Technology Data Exchange (ETDEWEB)
Jung, Florian
2012-07-16
In the present thesis, we study quantization of classical systems with non-trivial phase spaces using the group-theoretical quantization technique proposed by Isham. Our main goal is a better understanding of global and topological aspects of quantum theory. In practice, the group-theoretical approach enables direct quantization of systems subject to constraints and boundary conditions in a natural and physically transparent manner -- cases for which the canonical quantization method of Dirac fails. First, we provide a clarification of the quantization formalism. In contrast to prior treatments, we introduce a sharp distinction between the two group structures that are involved and explain their physical meaning. The benefit is a consistent and conceptually much clearer construction of the Canonical Group. In particular, we shed light upon the 'pathological' case for which the Canonical Group must be defined via a central Lie algebra extension and emphasise the role of the central extension in general. In addition, we study direct quantization of a particle restricted to a half-line with 'hard wall' boundary condition. Despite the apparent simplicity of this example, we show that a naive quantization attempt based on the cotangent bundle over the half-line as classical phase space leads to an incomplete quantum theory; the reflection which is a characteristic aspect of the 'hard wall' is not reproduced. Instead, we propose a different phase space that realises the necessary boundary condition as a topological feature and demonstrate that quantization yields a suitable quantum theory for the half-line model. The insights gained in the present special case improve our understanding of the relation between classical and quantum theory and illustrate how contact interactions may be incorporated.
Canonical group quantization and boundary conditions
International Nuclear Information System (INIS)
In the present thesis, we study quantization of classical systems with non-trivial phase spaces using the group-theoretical quantization technique proposed by Isham. Our main goal is a better understanding of global and topological aspects of quantum theory. In practice, the group-theoretical approach enables direct quantization of systems subject to constraints and boundary conditions in a natural and physically transparent manner -- cases for which the canonical quantization method of Dirac fails. First, we provide a clarification of the quantization formalism. In contrast to prior treatments, we introduce a sharp distinction between the two group structures that are involved and explain their physical meaning. The benefit is a consistent and conceptually much clearer construction of the Canonical Group. In particular, we shed light upon the 'pathological' case for which the Canonical Group must be defined via a central Lie algebra extension and emphasise the role of the central extension in general. In addition, we study direct quantization of a particle restricted to a half-line with 'hard wall' boundary condition. Despite the apparent simplicity of this example, we show that a naive quantization attempt based on the cotangent bundle over the half-line as classical phase space leads to an incomplete quantum theory; the reflection which is a characteristic aspect of the 'hard wall' is not reproduced. Instead, we propose a different phase space that realises the necessary boundary condition as a topological feature and demonstrate that quantization yields a suitable quantum theory for the half-line model. The insights gained in the present special case improve our understanding of the relation between classical and quantum theory and illustrate how contact interactions may be incorporated.
Evidence of non-canonical NOTCH signaling
DEFF Research Database (Denmark)
Traustadóttir, Gunnhildur Ásta; Jensen, Charlotte H; Thomassen, Mads;
2016-01-01
Dlk1(+/+) and Dlk1(-/-) mouse tissues at E16.5, we demonstrated that several NOTCH signaling pathways indeed are affected by DLK1 during tissue development, and this was supported by a lower activation of NOTCH1 protein in Dlk1(+/+) embryos. Likewise, but using a distinct Dlk1-manipulated (si......Canonical NOTCH signaling, known to be essential for tissue development, requires the Delta-Serrate-LAG2 (DSL) domain for NOTCH to interact with its ligand. However, despite lacking DSL, Delta-like 1 homolog (DLK1), a protein that plays a significant role in mammalian development, has been...
Kato expansion in quantum canonical perturbation theory
Nikolaev, Andrey
2016-06-01
This work establishes a connection between canonical perturbation series in quantum mechanics and a Kato expansion for the resolvent of the Liouville superoperator. Our approach leads to an explicit expression for a generator of a block-diagonalizing Dyson's ordered exponential in arbitrary perturbation order. Unitary intertwining of perturbed and unperturbed averaging superprojectors allows for a description of ambiguities in the generator and block-diagonalized Hamiltonian. We compare the efficiency of the corresponding computational algorithm with the efficiencies of the Van Vleck and Magnus methods for high perturbative orders.
Path integrals for arbitrary canonical transformations
International Nuclear Information System (INIS)
Some aspects of the path integral formulation of quantum mechanics are studied. This formalism is generalized to arbitrary canonical transformations, by means of an association between path integral probalility amplitudes and classical generators of transformations, analogous to the usual Hamiltonian time development phase space expression. Such association turns out to be equivalent to the Weyl quantization rule, and it is also shown that this formalism furnishes a path integral representation for a Lie algebra of a given set of classical generators. Some physical considerations about the path integral quantization procedure and about the relationship between classical and quantum dynamical structures are also discussed. (Author)
Belief propagation for graph partitioning
International Nuclear Information System (INIS)
We study the belief-propagation algorithm for the graph bi-partitioning problem, i.e. the ground state of the ferromagnetic Ising model at a fixed magnetization. Application of a message passing scheme to a model with a fixed global parameter is not banal and we show that the magnetization can in fact be fixed in a local way within the belief-propagation equations. Our method provides the full phase diagram of the bi-partitioning problem on random graphs, as well as an efficient heuristic solver that we anticipate to be useful in a wide range of application of the partitioning problem.
Present status of partitioning developments
International Nuclear Information System (INIS)
Evolution and development of the concept of partitioning of high-level liquid wastes (HLLW) in nuclear fuel reprocessing are reviewed historically from the early phase of separating useful radioisotopes from HLLW to the recent phase of eliminating hazardous nuclides such as transuranium elements for safe waste disposal. Since the criteria in determining the nuclides for elimination and the respective decontamination factors are important in the strategy of partitioning, current views on the criteria are summarized. As elimination of the transuranium is most significant in the partitioning, various methods available of separating them from fission products are evaluated. (auth.)
Square Partitions and Catalan Numbers
Bennett, Matthew; Chari, Vyjayanthi; Dolbin, R. J.; Manning, Nathan
2009-01-01
For each integer $k\\ge 1$, we define an algorithm which associates to a partition whose maximal value is at most $k$ a certain subset of all partitions. In the case when we begin with a partition $\\lambda$ which is square, i.e $\\lambda=\\lambda_1\\ge...\\ge\\lambda_k>0$, and $\\lambda_1=k,\\lambda_k=1$, then applying the algorithm $\\ell$ times gives rise to a set whose cardinality is either the Catalan number $c_{\\ell-k+1}$ (the self dual case) or twice the Catalan number. The algorithm defines a t...
Canonical-basis time-dependent Hartree-Fock-Bogoliubov theory and linear-response calculations
Ebata, Shuichiro; Inakura, Tsunenori; Yoshida, Kenichi; Hashimoto, Yukio; Yabana, Kazuhiro
2010-01-01
We present simple equations for a canonical-basis formulation of the time-dependent Hartree-Fock-Bogoliubov (TDHFB) theory. The equations are obtained from the TDHFB theory with an approximation that the pair potential is assumed to be diagonal in the canonical basis. The canonical-basis formulation significantly reduces the computational cost. We apply the method to linear-response calculations for even-even light nuclei and demonstrate its capability and accuracy by comparing our results with recent calculations of the quasi-particle random-phase approximation with Skyrme functionals. We show systematic studies of E1 strength distributions for Ne and Mg isotopes. The evolution of the low-lying pygmy strength seems to be determined by the interplay of several factors, including the neutron excess, separation energy, neutron shell effects, deformation, and pairing.
Development of partitioning method
International Nuclear Information System (INIS)
The present paper describes the examination of the possibility to improve denitration and extraction processes by adding oxalic acid in the partitioning process which has been developed for the purpose of separating high-level liquid waste (HLW) into a few groups of elements. First, the effect of oxalic acid in the denitration of HLW was examined to reduce the amount of the precipitate formed during the denitration. As a result, it was found that it was possible to reduce the precipitation of molybdenum, zirconium and tellurium. However, some elements precipitated at any concentration of oxalic acid. The addition of oxalic acid increased the amounts of precipitates of neodymium which was the representative of transuranic elements and strontium which was a troublesome element because of its heat generation. At the extraction process with DIDPA (diisodecyl phosphoric acid), oxalic acid was expected to prevent the third phase formation caused by iron, by making a complex with iron. However, the result showed that oxalic acid did not suppress the extraction of iron. The addition of oxalic acid was no effects on preventing the third phase formation. The influence of the presence of iron on the oxalate precipitation of rare earths was also examined in the present study. (author)
Partitioning ecosystems for sustainability.
Murray, Martyn G
2016-03-01
Decline in the abundance of renewable natural resources (RNRs) coupled with increasing demands of an expanding human population will greatly intensify competition for Earth's natural resources during this century, yet curiously, analytical approaches to the management of productive ecosystems (ecological theory of wildlife harvesting, tragedy of the commons, green economics, and bioeconomics) give only peripheral attention to the driving influence of competition on resource exploitation. Here, I apply resource competition theory (RCT) to the exploitation of RNRs and derive four general policies in support of their sustainable and equitable use: (1) regulate resource extraction technology to avoid damage to the resource base; (2) increase efficiency of resource use and reduce waste at every step in the resource supply chain and distribution network; (3) partition ecosystems with the harvesting niche as the basic organizing principle for sustainable management of natural resources by multiple users; and (4) increase negative feedback between consumer and resource to bring about long-term sustainable use. A simple policy framework demonstrates how RCT integrates with other elements of sustainability science to better manage productive ecosystems. Several problem areas of RNR management are discussed in the light of RCT, including tragedy of the commons, overharvesting, resource collapse, bycatch, single species quotas, and simplification of ecosystems. PMID:27209800
Incentives for partitioning, revisited
International Nuclear Information System (INIS)
The incentives for separating and eliminating various elements from radioactive waste prior to final geologic disposal were investigated. Exposure pathways to humans were defined, and potential radiation doses to an individual living within the region of influence of the underground storage site were calculated. The assumed radionuclide source was 1/5 of the accumulated high-level waste from the US nuclear power economy through the year 2000. The repository containing the waste was assumed to be located in a reference salt site geology. The study required numerous assumptions concerning the transport of radioactivity from the geologic storage site to man. The assumptions used maximized the estimated potential radiation doses, particularly in the case of the intrusion water well scenario, where hydrologic flow field dispersion effects were ignored. Thus, incentives for removing elements from the waste tended to be maximized. Incentives were also maximized by assuming that elements removed from the waste could be eliminated from the earth without risk. The results of the study indicate that for reasonable disposal conditions, incentives for partitioning any elements from the waste in order to minimize the risk to humans are marginal at best
An obstruction to the existence of anti-canonically balanced metrics on Fano manifolds
Saito, Shunsuke; Takahashi, Ryosuke
2016-01-01
We introduce a new obstruction to the existence of anti-canonically balanced metrics by studying the asymptotic behavior of the quantized Ding functional along Bergman geodesic rays associated to special test configurations. We also discuss some relation between our new stability and asymptotic Chow stability.
Definition of a time variable with entropy of a perfect fluid in canonical quantum gravity
International Nuclear Information System (INIS)
The Brown-Kuchar mechanism is applied in the case of general relativity coupled with Schutz' model for a perfect fluid. Using the canonical formalism and manipulating the set of modified constraints one is able to recover the definition of a time-evolution operator, i.e. a physical Hamiltonian, expressed as a functional of gravitational variables and the entropy.
Definition of a time variable with Entropy of a perfect fluid in Canonical Quantum Gravity
Cianfrani, Francesco; Montani, Giovanni; Zonetti, Simone
2008-01-01
The Brown-Kuchar mechanism is applied in the case of General Relativity coupled with the Schutz model for a perfect fluid. Using the canonical formalism and manipulating the set of modified constraints one is able to recover the definition of a time evolution operator, i.e. a physical Hamiltonian, expressed as a functional of gravitational variables and the entropy.
Site Partition: Turning One Site into Two for Adsorbing CO2.
Tian, Ziqi; Dai, Sheng; Jiang, De-En
2016-07-01
We propose the concept of site partition to explain the role of guest molecules in increasing CO2 uptake in metal-organic frameworks and to design new covalent porous materials for CO2 capture. From grand canonical Monte Carlo simulations of CO2 sorption in the recently synthesized CPM-33 MOFs, we show that guest insertion divides one open metal site into two relatively strong binding sites, hence dramatically increasing CO2 uptake. Further, we extend the site partition concept to covalent organic frameworks with large free volume. After insertion of a designed geometry-matching guest, we show that the volumetric uptake of CO2 doubles. Therefore, the concept of site partition can be used to engineer the pore space of nanoporous materials for higher gas uptake. PMID:27320252
Spectral partitioning in diffraction tomography
Energy Technology Data Exchange (ETDEWEB)
Lehman, S K; Chambers, D H; Candy, J V
1999-06-14
The scattering mechanism of diffraction tomography is described by the integral form of the Helmholtz equation. The goal of diffraction tomography is to invert this equation in order to reconstruct the object function from the measured scattered fields. During the forward propagation process, the spatial spectrum of the object under investigation is ''smeared,'' by a convolution in the spectral domain, across the propagating and evanescent regions of the received field. Hence, care must be taken in performing the reconstruction, as the object's spectral information has been moved into regions where it may be considered to be noise rather than useful information. This will reduce the quality and resolution of the reconstruction. We show haw the object's spectrum can be partitioned into resolvable and non-resolvable parts based upon the cutoff between the propagating and evanescent fields. Operating under the Born approximation, we develop a beam-forming on transmit approach to direct the energy into either the propagating or evanescent parts of the spectrum. In this manner, we may individually interrogate the propagating and evanescent regions of the object spectrum.
Face hallucination using orthogonal canonical correlation analysis
Zhou, Huiling; Lam, Kin-Man
2016-05-01
A two-step face-hallucination framework is proposed to reconstruct a high-resolution (HR) version of a face from an input low-resolution (LR) face, based on learning from LR-HR example face pairs using orthogonal canonical correlation analysis (orthogonal CCA) and linear mapping. In the proposed algorithm, face images are first represented using principal component analysis (PCA). Canonical correlation analysis (CCA) with the orthogonality property is then employed, to maximize the correlation between the PCA coefficients of the LR and the HR face pairs to improve the hallucination performance. The original CCA does not own the orthogonality property, which is crucial for information reconstruction. We propose using orthogonal CCA, which is proven by experiments to achieve a better performance in terms of global face reconstruction. In addition, in the residual-compensation process, a linear-mapping method is proposed to include both the inter- and intrainformation about manifolds of different resolutions. Compared with other state-of-the-art approaches, the proposed framework can achieve a comparable, or even better, performance in terms of global face reconstruction and the visual quality of face hallucination. Experiments on images with various parameter settings and blurring distortions show that the proposed approach is robust and has great potential for real-world applications.
New constraints for canonical general relativity
Reisenberger, M
1995-01-01
Ashtekar's canonical theory of classical complex Euclidean GR (no Lorentzian reality conditions) is found to be invariant under the full algebra of infinitesimal 4-diffeomorphisms, but non-invariant under some finite proper 4-diffeos when the densitized dreibein, \\tilE^a_i, is degenerate. The breakdown of 4-diffeo invariance appears to be due to the inability of the Ashtekar Hamiltonian to generate births and deaths of \\tilE flux loops (leaving open the possibility that a new `causality condition' forbidding the birth of flux loops might justify the non-invariance of the theory). A fully 4-diffeo invariant canonical theory in Ashtekar's variables, derived from Plebanski's action, is found to have constraints that are stronger than Ashtekar's for rank\\tilE < 2. The corresponding Hamiltonian generates births and deaths of \\tilE flux loops. It is argued that this implies a finite amplitude for births and deaths of loops in the physical states of quantum GR in the loop representation, thus modifying this (part...
Canonical Transformations can Dramatically Simplify Supersymmetry
Dixon, John
2016-01-01
A useful way to keep track of the SUSY invariance of a theory is by formulating it with a BRST Poisson Bracket. It turns out that there is a crucial subtlety that is hidden in this formulation. When the theory contains a Chiral Multiplet, the relevant BRST Poisson Bracket has a very important Canonical Transformation that leaves it invariant. This Canonical Transformation takes all or part of the Scalar Field $A$ and replaces it with a Zinn Source $J_A$, and also takes the related Zinn Source $\\Gamma_A$ and replaces it with an `Antighost' Field $\\eta_A$. Naively, this looks like it is just a change of notation. But in fact the interpretation means that one has moved some of the conserved Noether SUSY current from the Field Action, and placed it partly in the Zinn Sources Action, and so the SUSY current in the Field part of the Action is no longer conserved, because the Zinn Sources do not satisfy any equations of motion. They are not quantized, because they are Sources. So it needs to be recognized that SUSY ...
Bootstrap clustering for graph partitioning
Gambette, Philippe; Guénoche, Alain
2011-01-01
Given a simple undirected weighted or unweighted graph, we try to cluster the vertex set into communities and also to quantify the robustness of these clusters. For that task, we propose a new method, called bootstrap clustering which consists in (i) defining a new clustering algorithm for graphs, (ii) building a set of graphs similar to the initial one, (iii) applying the clustering method to each of them, making a profile (set) of partitions, (iv) computing a consensus partition for this pr...
Extension of warm inflation to non-canonical scalar fields
Zhang, Xiao-Min
2014-01-01
We extend the warm inflationary scenario to the case of the non-canonical scalar fields. The equation of motion and the other basic equations of this new scenario are obtained. The Hubble damped term is enhanced in non-canonical inflation. A linear stability analysis is performed to give the proper slow roll conditions in warm non-canonical inflation. We study the density fluctuations in the new picture and obtain an approximate analytic expression of the power spectrum. The energy scale at the horizon crossing is depressed by both non-canonical effect and thermal effect, so does the tensor-to-scalar ratio. Besides the synergy, the non-canonical effect and the thermal effect are competing in the case of the warm non-canonical inflation.
[Huang Yizhou's study on Nei jing (Inner Canon)].
Hu, Benxiang; Huang, Youmei; Yu, Chengfen
2002-01-01
Being a great classical scholar of the late Qing dynasty, Huang Yizhou collated Nei jing (Inner Canon) by textual criticism. But most of his works were missing. By reviewing historical documents and literature, it has been found that his collated books include Huang di nei jing su wen jiao ben (Collated Edition of Huangdi's Inner Canon Plain Questions), Huang di nei jing su wen chong jiao zheng (Recollated Huangdi's Inner Canon Plain Questions), Nei jing zhen ci (Acupuncture in Inner Canon), Huang di nei jing jiu juan ji zhu (Variorum of Nine Volumes of Huangdi's Inner Canon), Huang di nei jing ming tang (Acupuncture Chart of Huangdi's Inner Canon), and Jiu chao tai su jiao ben (Old Extremely Plain Question Recension). Many of his disciples became famous scholars in the Republican period. PMID:12015056
Energy-Aware Task Partitioning on Heterogeneous Multiprocessor Platforms
Saad, Elsayed; Shalan, Mohamed; Elewi, Abdullah
2012-01-01
Efficient task partitioning plays a crucial role in achieving high performance at multiprocessor plat forms. This paper addresses the problem of energy-aware static partitioning of periodic real-time tasks on heterogeneous multiprocessor platforms. A Particle Swarm Optimization variant based on Min-min technique for task partitioning is proposed. The proposed approach aims to minimize the overall energy consumption, meanwhile avoid deadline violations. An energy-aware cost function is proposed to be considered in the proposed approach. Extensive simulations and comparisons are conducted in order to validate the effectiveness of the proposed technique. The achieved results demonstrate that the proposed partitioning scheme significantly surpasses previous approaches in terms of both number of iterations and energy savings.
Optimal Partitioning and Granularity of Uniform Task Grkaphs
Institute of Scientific and Technical Information of China (English)
章中云; 李国杰
1991-01-01
Task partitioning is an important technique in parallel processing.In this paper,we investigate the optimal partitioning strategies and granularities of tasks with communications based on several models of parallel computer systems.Different from the usual approach,we study the optimal partitioning strategies and granularities from the viewpoint of minimizing T as well as minimizing NT2,where N is the number of processors used and T is the program execution time using N processors.Our results show that the optimal partitioning strategies for all cases discussed in this paper are the same--either to assign all tasks to one processor or to distribute them among the processors as equally as possible depending only on the functions of ratio of running time to communication time R/C.
An unconventional canonical quantization of local field theories
International Nuclear Information System (INIS)
The conventional extension of the canonical quantization for the local field theories leads to serious mathematical and physical problems (ultraviolet catastrophes and instability of the vacuum). A new proposed method of this extension exploits maximally the principle of locality. Identical copies of the quantum counterparts of the classical mechanical system are placed at each points of a hyperspace of fixed time. The global system is synthetized by quantum statistical method. The argument of wave function, the field operator does not depend explicitely on the point of the space-time. In the perturbation theory the interaction Hamiltonian is now not global but local, thus the usual ultraviolet divergences do not appear. This formalism is an explicite example that the quantum dynamics of a system can be locally implemented, according to the physical measuring situation. (D. Gy.)
On two mathematical problems of canonical quantization. IV
International Nuclear Information System (INIS)
A method for solving the problem of reconstructing a measure beginning with its logarithmic derivative is presented. The method completes that of solving the stochastic differential equation via Dirichlet forms proposed by S. Albeverio and M. Rockner. As a result one obtains the mathematical apparatus for the stochastic quantization. The apparatus is applied to prove the existence of the Feynman-Kac measure of the sine-Gordon and λφ2n/(1 + κ2φ2n)-models. A synthesis of both mathematical problems of canonical quantization is obtained in the form of a second-order martingale problem for vacuum noise. It is shown that in stochastic mechanics the martingale problem is an analog of Newton's second law and enables us to find the Nelson's stochastic trajectories without determining the wave functions. 33 refs
A NOVEL ALGORITHM FOR VOICE CONVERSION USING CANONICAL CORRELATION ANALYSIS
Institute of Scientific and Technical Information of China (English)
Jian Zhihua; Yang Zhen
2008-01-01
A novel algorithm for voice conversion is proposed in this paper. The mapping function of spectral vectors of the source and target speakers is calculated by the Canonical Correlation Analysis(CCA) estimation based on Gaussian mixture models. Since the spectral envelope feature remains a majority of second order statistical information contained in speech after Linear Prediction Coding(LPC) analysis, the CCA method is more suitable for spectral conversion than Minimum Mean Square Error (MMSE) because CCA explicitly considers the variance of each component of the spectral vectors during conversion procedure. Both objective evaluations and subjective listening tests are conducted. The experimental results demonstrate that the proposed scheme can achieve better performance than the previous method which uses MMSE estimation criterion.
Integral Canonical Models for Automorphic Vector Bundles of Abelian Type
Lovering, Tom
2016-01-01
We define and construct integral canonical models for automorphic vector bundles over Shimura varieties of abelian type. More precisely, we first build on Kisin's work to construct integral canonical models over rings of integers of number fields with finitely many primes inverted for Shimura varieties of abelian type with hyperspecial level at all primes we do not invert, compatible with Kisin's construction. We then define a notion of an integral canonical model for the standard principal b...
Intersubject information mapping: revealing canonical representations of complex natural stimuli
Directory of Open Access Journals (Sweden)
Nikolaus Kriegeskorte
2015-03-01
Full Text Available Real-world time-continuous stimuli such as video promise greater naturalism for studies of brain function. However, modeling the stimulus variation is challenging and introduces a bias in favor of particular descriptive dimensions. Alternatively, we can look for brain regions whose signal is correlated between subjects, essentially using one subject to model another. Intersubject correlation mapping (ICM allows us to find brain regions driven in a canonical manner across subjects by a complex natural stimulus. However, it requires a direct voxel-to-voxel match between the spatiotemporal activity patterns and is thus only sensitive to common activations sufficiently extended to match up in Talairach space (or in an alternative, e.g. cortical-surface-based, common brain space. Here we introduce the more general approach of intersubject information mapping (IIM. For each brain region, IIM determines how much information is shared between the subjects' local spatiotemporal activity patterns. We estimate the intersubject mutual information using canonical correlation analysis applied to voxels within a spherical searchlight centered on each voxel in turn. The intersubject information estimate is invariant to linear transforms including spatial rearrangement of the voxels within the searchlight. This invariance to local encoding will be crucial in exploring fine-grained brain representations, which cannot be matched up in a common space and, more fundamentally, might be unique to each individual – like fingerprints. IIM yields a continuous brain map, which reflects intersubject information in fine-grained patterns. Performed on data from functional magnetic resonance imaging (fMRI of subjects viewing the same television show, IIM and ICM both highlighted sensory representations, including primary visual and auditory cortices. However, IIM revealed additional regions in higher association cortices, namely temporal pole and orbitofrontal cortex. These
The Geometry of Tangent Bundles: Canonical Vector Fields
Directory of Open Access Journals (Sweden)
Tongzhu Li
2013-01-01
Full Text Available A canonical vector field on the tangent bundle is a vector field defined by an invariant coordinate construction. In this paper, a complete classification of canonical vector fields on tangent bundles, depending on vector fields defined on their bases, is obtained. It is shown that every canonical vector field is a linear combination with constant coefficients of three vector fields: the variational vector field (canonical lift, the Liouville vector field, and the vertical lift of a vector field on the base of the tangent bundle.
Partition of polycyclic aromatic hydrocarbons on organobentonites
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
A series of organobentonites synthesized by exchanging organiccation such as dodecyltri-methylammonium (DTMA),benzyldimethyltetradecylammonium (BDTDA), cetyltrimethyl-ammonium (CTMA), octodeyltrimethylammonium (OTMA) on bentonite. The optimal condition, properties and mechanisms for the organobentonites to sorb phenanthrene, anthracene, naphthalene, acenaphthene in water were investigated in detail. The partition behavior was determined for four polycyclic aromatic hydrocarbons (PAHs), such as naphthalene, phenanthrene, anthracene and acenaphthene, from water to a series of organobentonites. The interlayer spacings and organic carbon contents of organobentonites, removal rate and sorption capacities for organobentonites to treat phenanthrene,anthracene, naphthalene, acenaphthene were correlated to the length of alkyl chains and the amounts of cation surfactant exchanged on Foundation item: the bentonite. Phenanthrene, anthracene, naphthalene, and acenaphthene sorption to organobentonites were characterized by linear isotherms, indicating solute partition between water and the organic phase composed of the large alkyl functional groups of quaternary ammonium cations. PAHs distribution coefficients (Kd)between organobentonites and water were proportional to the organic carbon contents of organobentonites. However, the partition coefficients (Koc) were nearly constants for PAHs in the system of organobentonite-water. The Koc of phenanthrene, anthracene,naphthalene, acenaphthene were 2.621x105, 2.106x105, 2.247x104,5.085x104, respectively. The means Koc values on the organobentonites are about ten to twenty times larger than the values on the soils/sediments, what is significant prerequisite for organobentonite to apply to remediation of pollution soil and groundwater. The sorption mechanism was also evaluated from octanol-water partition coefficients and aqueous solubility of PAHs. The correlations between lgKoc and 1gkow, 1gKoc and 1gS for PAHs in the system of water